Least Common Multiple (LCM) of 37 and 117
The least common multiple (LCM) of 37 and 117 is 4329.
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 37 and 117?
First, calculate the GCD of 37 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 117 = 0 remainder 37 |
| 2 | 117 ÷ 37 = 3 remainder 6 |
| 3 | 37 ÷ 6 = 6 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 125 | 500 |
| 198 and 121 | 2178 |
| 21 and 108 | 756 |
| 133 and 130 | 17290 |
| 26 and 91 | 182 |