Mastering Highest Common Factor (HCF) and Least Common Multiple (LCM) is key to solving complex problems in fractions, time & work, and number theory.
Also known as GCD (Greatest Common Divisor). It is the largest number that divides two or more numbers without leaving a remainder.
Break numbers into prime factors and multiply the common factors with the lowest power.
Find HCF of 24 and 36:
$24 = 2^3 \times 3^1$
$36 = 2^2 \times 3^2$
HCF = $2^2 \times 3^1 = 4 \times 3 = 12$
The smallest positive number that is a multiple of two or more numbers. It is divisible by all the given numbers.
Take all prime factors involved, with their highest power.
Find LCM of 12 and 15:
$12 = 2^2 \times 3^1$
$15 = 3^1 \times 5^1$
LCM = $2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 = 60$
For any two numbers A and B:
Note: Does not apply to 3 numbers directly.
Formula:
Formula:
30 Questions focusing on Highest Common Factors, Division Method, and Word Problems.
30 Questions focusing on Least Common Multiples, Intervals, and Fraction Logic.