Least Common Multiple (LCM) of 117 and 12
The least common multiple (LCM) of 117 and 12 is 468.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 117 and 12?
First, calculate the GCD of 117 and 12 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 12 = 9 remainder 9 |
| 2 | 12 ÷ 9 = 1 remainder 3 |
| 3 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 105 | 12180 |
| 36 and 23 | 828 |
| 171 and 186 | 10602 |
| 26 and 54 | 702 |
| 57 and 102 | 1938 |