Least Common Multiple (LCM) of 120 and 172
The least common multiple (LCM) of 120 and 172 is 5160.
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 120 and 172?
First, calculate the GCD of 120 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 172 = 0 remainder 120 |
| 2 | 172 ÷ 120 = 1 remainder 52 |
| 3 | 120 ÷ 52 = 2 remainder 16 |
| 4 | 52 ÷ 16 = 3 remainder 4 |
| 5 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 37 | 555 |
| 156 and 46 | 3588 |
| 169 and 51 | 8619 |
| 199 and 79 | 15721 |
| 136 and 139 | 18904 |