Least Common Multiple (LCM) of 137 and 156
The least common multiple (LCM) of 137 and 156 is 21372.
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 156?
First, calculate the GCD of 137 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 156 = 0 remainder 137 |
| 2 | 156 ÷ 137 = 1 remainder 19 |
| 3 | 137 ÷ 19 = 7 remainder 4 |
| 4 | 19 ÷ 4 = 4 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 128 | 21120 |
| 115 and 74 | 8510 |
| 72 and 160 | 1440 |
| 58 and 196 | 5684 |
| 135 and 152 | 20520 |