LCM (Least Common Multiple) Calculation

LCM (Least Common Multiple) Calculation

LCM of Numbers

The Least Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both. We can find the LCM by either listing multiples or using the prime factorization method.

Example 1: LCM of 4 and 5

Step 1: List the multiples of 4: 4, 8, 12, 16, 20, 24…

Step 2: List the multiples of 5: 5, 10, 15, 20, 25…

Step 3: The smallest common multiple is 20.

Thus, LCM(4, 5) = 20.

Example 2: LCM of 6 and 8

Step 1: List the multiples of 6: 6, 12, 18, 24, 30, 36…

Step 2: List the multiples of 8: 8, 16, 24, 32…

Step 3: The smallest common multiple is 24.

Thus, LCM(6, 8) = 24.

Example 3: LCM of 9 and 12

Step 1: List the multiples of 9: 9, 18, 27, 36, 45…

Step 2: List the multiples of 12: 12, 24, 36, 48…

Step 3: The smallest common multiple is 36.

Thus, LCM(9, 12) = 36.

Example 4: LCM of 15 and 20

Step 1: List the multiples of 15: 15, 30, 45, 60, 75…

Step 2: List the multiples of 20: 20, 40, 60, 80…

Step 3: The smallest common multiple is 60.

Thus, LCM(15, 20) = 60.

Example 5: LCM of 7 and 11

Step 1: List the multiples of 7: 7, 14, 21, 28, 35…

Step 2: List the multiples of 11: 11, 22, 33, 44…

Step 3: The smallest common multiple is 77.

Thus, LCM(7, 11) = 77.

Example 6: LCM of 8 and 14

Step 1: List the multiples of 8: 8, 16, 24, 32, 40…

Step 2: List the multiples of 14: 14, 28, 42, 56…

Step 3: The smallest common multiple is 56.

Thus, LCM(8, 14) = 56.

Example 7: LCM of 10 and 25

Step 1: List the multiples of 10: 10, 20, 30, 40, 50…

Step 2: List the multiples of 25: 25, 50, 75…

Step 3: The smallest common multiple is 50.

Thus, LCM(10, 25) = 50.

Example 8: LCM of 5 and 7

Step 1: List the multiples of 5: 5, 10, 15, 20, 25…

Step 2: List the multiples of 7: 7, 14, 21, 28…

Step 3: The smallest common multiple is 35.

Thus, LCM(5, 7) = 35.

Example 9: LCM of 12 and 18

Step 1: List the multiples of 12: 12, 24, 36, 48…

Step 2: List the multiples of 18: 18, 36, 54…

Step 3: The smallest common multiple is 36.

Thus, LCM(12, 18) = 36.

Example 10: LCM of 3 and 8

Step 1: List the multiples of 3: 3, 6, 9, 12, 15…

Step 2: List the multiples of 8: 8, 16, 24, 32…

Step 3: The smallest common multiple is 24.

Thus, LCM(3, 8) = 24.

Example 11: LCM of 18 and 24

Step 1: List the multiples of 18: 18, 36, 54, 72, 90…

Step 2: List the multiples of 24: 24, 48, 72, 96…

Step 3: The smallest common multiple is 72.

Thus, LCM(18, 24) = 72.

Example 12: LCM of 7 and 9

Step 1: List the multiples of 7: 7, 14, 21, 28, 35…

Step 2: List the multiples of 9: 9, 18, 27, 36, 45…

Step 3: The smallest common multiple is 63.

Thus, LCM(7, 9) = 63.

Example 13: LCM of 8 and 16

Step 1: List the multiples of 8: 8, 16, 24, 32, 40…

Step 2: List the multiples of 16: 16, 32, 48…

Step 3: The smallest common multiple is 16.

Thus, LCM(8, 16) = 16.

Example 14: LCM of 14 and 21

Step 1: List the multiples of 14: 14, 28, 42, 56…

Step 2: List the multiples of 21: 21, 42, 63…

Step 3: The smallest common multiple is 42.

Thus, LCM(14, 21) = 42.

Example 15: LCM of 5 and 15

Step 1: List the multiples of 5: 5, 10, 15, 20…

Step 2: List the multiples of 15: 15, 30, 45…

Step 3: The smallest common multiple is 15.

Thus, LCM(5, 15) = 15.

Example 16: LCM of 18 and 30

Step 1: List the multiples of 18: 18, 36, 54, 72…

Step 2: List the multiples of 30: 30, 60, 90…

Step 3: The smallest common multiple is 90.

Thus, LCM(18, 30) = 90.

Example 17: LCM of 9 and 11

Step 1: List the multiples of 9: 9, 18, 27, 36…

Step 2: List the multiples of 11: 11, 22, 33, 44…

Step 3: The smallest common multiple is 99.

Thus, LCM(9, 11) = 99.

Example 18: LCM of 20 and 25

Step 1: List the multiples of 20: 20, 40, 60, 80…

Step 2: List the multiples of 25: 25, 50, 75, 100…

Step 3: The smallest common multiple is 100.

Thus, LCM(20, 25) = 100.

Example 19: LCM of 12 and 36

Step 1: List the multiples of 12: 12, 24, 36, 48…

Step 2: List the multiples of 36: 36, 72, 108…

Step 3: The smallest common multiple is 36.

Thus, LCM(12, 36) = 36.

Example 20: LCM of 22 and 44

Step 1: List the multiples of 22: 22, 44, 66…

Step 2: List the multiples of 44: 44, 88…

Step 3: The smallest common multiple is 44.

Thus, LCM(22, 44) = 44.

Example 21: LCM of 24 and 36

Step 1: List the multiples of 24: 24, 48, 72, 96…

Step 2: List the multiples of 36: 36, 72, 108…

Step 3: The smallest common multiple is 72.

Thus, LCM(24, 36) = 72.

Example 22: LCM of 8 and 21

Step 1: List the multiples of 8: 8, 16, 24, 32…

Step 2: List the multiples of 21: 21, 42, 63…

Step 3: The smallest common multiple is 168.

Thus, LCM(8, 21) = 168.

Example 23: LCM of 11 and 22

Step 1: List the multiples of 11: 11, 22, 33, 44…

Step 2: List the multiples of 22: 22, 44, 66…

Step 3: The smallest common multiple is 22.

Thus, LCM(11, 22) = 22.

Example 24: LCM of 14 and 25

Step 1: List the multiples of 14: 14, 28, 42, 56…

Step 2: List the multiples of 25: 25, 50, 75…

Step 3: The smallest common multiple is 350.

Thus, LCM(14, 25) = 350.

Example 25: LCM of 20 and 30

Step 1: List the multiples of 20: 20, 40, 60, 80…

Step 2: List the multiples of 30: 30, 60, 90…

Step 3: The smallest common multiple is 60.

Thus, LCM(20, 30) = 60.

Example 26: LCM of 5 and 9

Step 1: List the multiples of 5: 5, 10, 15, 20…

Step 2: List the multiples of 9: 9, 18, 27…

Step 3: The smallest common multiple is 45.

Thus, LCM(5, 9) = 45.

Example 27: LCM of 18 and 25

Step 1: List the multiples of 18: 18, 36, 54, 72…

Step 2: List the multiples of 25: 25, 50, 75…

Step 3: The smallest common multiple is 450.

Thus, LCM(18, 25) = 450.

Example 28: LCM of 3 and 10

Step 1: List the multiples of 3: 3, 6, 9, 12…

Step 2: List the multiples of 10: 10, 20, 30…

Step 3: The smallest common multiple is 30.

Thus, LCM(3, 10) = 30.

Example 29: LCM of 5 and 25

Step 1: List the multiples of 5: 5, 10, 15, 20, 25…

Step 2: List the multiples of 25: 25, 50, 75…

Step 3: The smallest common multiple is 25.

Thus, LCM(5, 25) = 25.

Example 30: LCM of 14 and 35

Step 1: List the multiples of 14: 14, 28, 42, 56…

Step 2: List the multiples of 35: 35, 70, 105…

Step 3: The smallest common multiple is 70.

Thus, LCM(14, 35) = 70.

Example 31: LCM of 25 and 40

Step 1: List the multiples of 25: 25, 50, 75, 100…

Step 2: List the multiples of 40: 40, 80, 120…

Step 3: The smallest common multiple is 200.

Thus, LCM(25, 40) = 200.

Example 32: LCM of 18 and 30

Step 1: List the multiples of 18: 18, 36, 54, 72…

Step 2: List the multiples of 30: 30, 60, 90…

Step 3: The smallest common multiple is 90.

Thus, LCM(18, 30) = 90.

Example 33: LCM of 6 and 15

Step 1: List the multiples of 6: 6, 12, 18, 24…

Step 2: List the multiples of 15: 15, 30, 45…

Step 3: The smallest common multiple is 30.

Thus, LCM(6, 15) = 30.

Example 34: LCM of 7 and 10

Step 1: List the multiples of 7: 7, 14, 21, 28…

Step 2: List the multiples of 10: 10, 20, 30…

Step 3: The smallest common multiple is 70.

Thus, LCM(7, 10) = 70.

Example 35: LCM of 8 and 24

Step 1: List the multiples of 8: 8, 16, 24, 32…

Step 2: List the multiples of 24: 24, 48…

Step 3: The smallest common multiple is 24.

Thus, LCM(8, 24) = 24.

Example 36: LCM of 9 and 15

Step 1: List the multiples of 9: 9, 18, 27, 36…

Step 2: List the multiples of 15: 15, 30, 45…

Step 3: The smallest common multiple is 45.

Thus, LCM(9, 15) = 45.

Example 37: LCM of 10 and 45

Step 1: List the multiples of 10: 10, 20, 30, 40…

Step 2: List the multiples of 45: 45, 90, 135…

Step 3: The smallest common multiple is 90.

Thus, LCM(10, 45) = 90.

Example 38: LCM of 12 and 15

Step 1: List the multiples of 12: 12, 24, 36, 48…

Step 2: List the multiples of 15: 15, 30, 45…

Step 3: The smallest common multiple is 60.

Thus, LCM(12, 15) = 60.

Example 39: LCM of 17 and 19

Step 1: List the multiples of 17: 17, 34, 51, 68…

Step 2: List the multiples of 19: 19, 38, 57, 76…

Step 3: The smallest common multiple is 323.

Thus, LCM(17, 19) = 323.

Example 40: LCM of 14 and 18

Step 1: List the multiples of 14: 14, 28, 42…

Step 2: List the multiples of 18: 18, 36, 54…

Step 3: The smallest common multiple is 126.

Thus, LCM(14, 18) = 126.

Example 41: LCM of 9 and 20

Step 1: List the multiples of 9: 9, 18, 27, 36…

Step 2: List the multiples of 20: 20, 40, 60…

Step 3: The smallest common multiple is 180.

Thus, LCM(9, 20) = 180.

Example 42: LCM of 12 and 30

Step 1: List the multiples of 12: 12, 24, 36, 48…

Step 2: List the multiples of 30: 30, 60, 90…

Step 3: The smallest common multiple is 60.

Thus, LCM(12, 30) = 60.

Example 43: LCM of 8 and 18

Step 1: List the multiples of 8: 8, 16, 24, 32…

Step 2: List the multiples of 18: 18, 36, 54…

Step 3: The smallest common multiple is 72.

Thus, LCM(8, 18) = 72.

Example 44: LCM of 20 and 40

Step 1: List the multiples of 20: 20, 40, 60…

Step 2: List the multiples of 40: 40, 80…

Step 3: The smallest common multiple is 40.

Thus, LCM(20, 40) = 40.

Example 45: LCM of 11 and 33

Step 1: List the multiples of 11: 11, 22, 33…

Step 2: List the multiples of 33: 33, 66…

Step 3: The smallest common multiple is 33.

Thus, LCM(11, 33) = 33.

Example 46: LCM of 30 and 45

Step 1: List the multiples of 30: 30, 60, 90, 120…

Step 2: List the multiples of 45: 45, 90, 135…

Step 3: The smallest common multiple is 90.

Thus, LCM(30, 45) = 90.

Example 47: LCM of 6 and 28

Step 1: List the multiples of 6: 6, 12, 18, 24, 30…

Step 2: List the multiples of 28: 28, 56, 84…

Step 3: The smallest common multiple is 84.

Thus, LCM(6, 28) = 84.

Example 48: LCM of 7 and 24

Step 1: List the multiples of 7: 7, 14, 21, 28…

Step 2: List the multiples of 24: 24, 48, 72…

Step 3: The smallest common multiple is 168.

Thus, LCM(7, 24) = 168.

Example 49: LCM of 13 and 17

Step 1: List the multiples of 13: 13, 26, 39, 52…

Step 2: List the multiples of 17: 17, 34, 51, 68…

Step 3: The smallest common multiple is 221.

Thus, LCM(13, 17) = 221.

Example 50: LCM of 16 and 25

Step 1: List the multiples of 16: 16, 32, 48, 64…

Step 2: List the multiples of 25: 25, 50, 75…

Step 3: The smallest common multiple is 400.

Thus, LCM(16, 25) = 400.

🌙