Least Common Multiple (LCM) of 117 and 15
The least common multiple (LCM) of 117 and 15 is 585.
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 15?
First, calculate the GCD of 117 and 15 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 15 = 7 remainder 12 |
| 2 | 15 ÷ 12 = 1 remainder 3 |
| 3 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 172 | 172 |
| 138 and 166 | 11454 |
| 103 and 154 | 15862 |
| 153 and 76 | 11628 |
| 149 and 102 | 15198 |