About lcm calculator
The lowest common multiple (LCM) is the smallest number that all the given numbers divide into exactly.
Method
Use prime factorisation: take each prime at its highest power. 12 = 2² × 3 and 18 = 2 × 3², so the LCM is 2² × 3² = 36.
Where it is used
Adding fractions with different denominators, and finding when repeating events line up, such as two buses that arrive every 12 and 18 minutes meeting again after 36 minutes.
A worked example
To find the LCM of 12, 18 and 30, write 12 = 2² × 3, 18 = 2 × 3² and 30 = 2 × 3 × 5. Take the highest power of each prime: 2² × 3² × 5 = 180. Three lights blinking every 12, 18 and 30 seconds all blink together every 180 seconds.
Connection with GCD
For two numbers, LCM × GCD equals their product. The LCM of 12 and 18 is 36 and the GCD is 6, and 36 × 6 = 216 = 12 × 18.
