Least Common Multiple (LCM) of 137 and 157
The least common multiple (LCM) of 137 and 157 is 21509.
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 157?
First, calculate the GCD of 137 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 157 = 0 remainder 137 |
| 2 | 157 ÷ 137 = 1 remainder 20 |
| 3 | 137 ÷ 20 = 6 remainder 17 |
| 4 | 20 ÷ 17 = 1 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 160 | 1120 |
| 13 and 193 | 2509 |
| 175 and 115 | 4025 |
| 15 and 162 | 810 |
| 113 and 148 | 16724 |