Least Common Multiple (LCM) of 135 and 172
The least common multiple (LCM) of 135 and 172 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 135 and 172?
First, calculate the GCD of 135 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 172 = 0 remainder 135 |
| 2 | 172 ÷ 135 = 1 remainder 37 |
| 3 | 135 ÷ 37 = 3 remainder 24 |
| 4 | 37 ÷ 24 = 1 remainder 13 |
| 5 | 24 ÷ 13 = 1 remainder 11 |
| 6 | 13 ÷ 11 = 1 remainder 2 |
| 7 | 11 ÷ 2 = 5 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 178 | 3382 |
| 109 and 93 | 10137 |
| 156 and 146 | 11388 |
| 178 and 187 | 33286 |
| 142 and 164 | 11644 |