Least Common Multiple (LCM) of 137 and 96
The least common multiple (LCM) of 137 and 96 is 13152.
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 96?
First, calculate the GCD of 137 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 96 = 1 remainder 41 |
| 2 | 96 ÷ 41 = 2 remainder 14 |
| 3 | 41 ÷ 14 = 2 remainder 13 |
| 4 | 14 ÷ 13 = 1 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 187 | 5797 |
| 168 and 67 | 11256 |
| 25 and 119 | 2975 |
| 193 and 117 | 22581 |
| 185 and 139 | 25715 |