Least Common Multiple (LCM) of 172 and 137
The least common multiple (LCM) of 172 and 137 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 172 and 137?
First, calculate the GCD of 172 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 137 = 1 remainder 35 |
| 2 | 137 ÷ 35 = 3 remainder 32 |
| 3 | 35 ÷ 32 = 1 remainder 3 |
| 4 | 32 ÷ 3 = 10 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 28 | 420 |
| 146 and 166 | 12118 |
| 25 and 63 | 1575 |
| 200 and 113 | 22600 |
| 157 and 82 | 12874 |