Least Common Multiple (LCM) of 117 and 37
The least common multiple (LCM) of 117 and 37 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 117 and 37?
First, calculate the GCD of 117 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 37 = 3 remainder 6 |
| 2 | 37 ÷ 6 = 6 remainder 1 |
| 3 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 19 | 684 |
| 85 and 132 | 11220 |
| 60 and 178 | 5340 |
| 161 and 154 | 3542 |
| 43 and 11 | 473 |