Least Common Multiple (LCM) of 117 and 132
The least common multiple (LCM) of 117 and 132 is 5148.
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 132?
First, calculate the GCD of 117 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 132 = 0 remainder 117 |
| 2 | 132 ÷ 117 = 1 remainder 15 |
| 3 | 117 ÷ 15 = 7 remainder 12 |
| 4 | 15 ÷ 12 = 1 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 99 | 7524 |
| 11 and 187 | 187 |
| 11 and 172 | 1892 |
| 45 and 108 | 540 |
| 38 and 139 | 5282 |