Least Common Multiple (LCM) of 120 and 75
The least common multiple (LCM) of 120 and 75 is 600.
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 75?
First, calculate the GCD of 120 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 75 = 1 remainder 45 |
| 2 | 75 ÷ 45 = 1 remainder 30 |
| 3 | 45 ÷ 30 = 1 remainder 15 |
| 4 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 59 | 11682 |
| 137 and 172 | 23564 |
| 78 and 68 | 2652 |
| 138 and 179 | 24702 |
| 111 and 164 | 18204 |