Least Common Multiple (LCM) of 137 and 76
The least common multiple (LCM) of 137 and 76 is 10412.
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 76?
First, calculate the GCD of 137 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 76 = 1 remainder 61 |
| 2 | 76 ÷ 61 = 1 remainder 15 |
| 3 | 61 ÷ 15 = 4 remainder 1 |
| 4 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 61 | 1403 |
| 103 and 17 | 1751 |
| 176 and 52 | 2288 |
| 143 and 66 | 858 |
| 129 and 102 | 4386 |