Least Common Multiple (LCM) of 172 and 135
The least common multiple (LCM) of 172 and 135 is 23220.
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 135?
First, calculate the GCD of 172 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 135 = 1 remainder 37 |
| 2 | 135 ÷ 37 = 3 remainder 24 |
| 3 | 37 ÷ 24 = 1 remainder 13 |
| 4 | 24 ÷ 13 = 1 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 85 | 13515 |
| 21 and 65 | 1365 |
| 39 and 120 | 1560 |
| 189 and 36 | 756 |
| 108 and 52 | 1404 |