Least Common Multiple (LCM) of 120 and 179
The least common multiple (LCM) of 120 and 179 is 21480.
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 179?
First, calculate the GCD of 120 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 179 = 0 remainder 120 |
| 2 | 179 ÷ 120 = 1 remainder 59 |
| 3 | 120 ÷ 59 = 2 remainder 2 |
| 4 | 59 ÷ 2 = 29 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 84 | 3612 |
| 101 and 129 | 13029 |
| 188 and 120 | 5640 |
| 169 and 14 | 2366 |
| 135 and 56 | 7560 |