LCM & HCF Calculator

LCM and HCF by prime factorisation

Example with 12, 18 and 30:

• 12 = 2 × 2 × 3
• 18 = 2 × 3 × 3
• 30 = 2 × 3 × 5

HCF = product of factors common to all = 2 × 3 = 6.
LCM = each prime at its highest power = 2² × 3² × 5 = 180.

Useful facts

• For two numbers, LCM × HCF = product of the numbers.
• HCF is also called GCD (greatest common divisor) or GCF.
• Use HCF to simplify fractions and ratios; use LCM to add fractions and solve "when will they meet again" problems.

Word problem

Two bells ring every 12 and 18 minutes. When do they ring together again? LCM(12, 18) = 36 minutes.

Frequently asked questions

What is the LCM of 12 and 18?

36. The HCF is 6, and 6 × 36 = 216 = 12 × 18.

What is the difference between LCM and HCF?

HCF is the largest number that divides all given numbers; LCM is the smallest number that all of them divide into.

Can I find LCM and HCF of more than two numbers?

Yes — enter as many numbers as you like, separated by commas.