Least Common Multiple (LCM) of 120 and 59
The least common multiple (LCM) of 120 and 59 is 7080.
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 59?
First, calculate the GCD of 120 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 59 = 2 remainder 2 |
| 2 | 59 ÷ 2 = 29 remainder 1 |
| 3 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 190 | 34770 |
| 106 and 110 | 5830 |
| 182 and 42 | 546 |
| 121 and 120 | 14520 |
| 20 and 29 | 580 |