Least Common Multiple (LCM) of 137 and 169
The least common multiple (LCM) of 137 and 169 is 23153.
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 169?
First, calculate the GCD of 137 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 169 = 0 remainder 137 |
| 2 | 169 ÷ 137 = 1 remainder 32 |
| 3 | 137 ÷ 32 = 4 remainder 9 |
| 4 | 32 ÷ 9 = 3 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 36 | 108 |
| 26 and 21 | 546 |
| 90 and 78 | 1170 |
| 76 and 142 | 5396 |
| 148 and 63 | 9324 |