Least Common Multiple (LCM) of 137 and 172
The least common multiple (LCM) of 137 and 172 is 23564.
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 172?
First, calculate the GCD of 137 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 172 = 0 remainder 137 |
| 2 | 172 ÷ 137 = 1 remainder 35 |
| 3 | 137 ÷ 35 = 3 remainder 32 |
| 4 | 35 ÷ 32 = 1 remainder 3 |
| 5 | 32 ÷ 3 = 10 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 136 | 6120 |
| 16 and 116 | 464 |
| 166 and 179 | 29714 |
| 110 and 109 | 11990 |
| 187 and 89 | 16643 |