Least Common Multiple (LCM) of 137 and 61
The least common multiple (LCM) of 137 and 61 is 8357.
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 137 and 61?
First, calculate the GCD of 137 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 61 = 2 remainder 15 |
| 2 | 61 ÷ 15 = 4 remainder 1 |
| 3 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 154 | 12320 |
| 117 and 115 | 13455 |
| 89 and 56 | 4984 |
| 129 and 78 | 3354 |
| 168 and 36 | 504 |