Least Common Multiple (LCM) of 75 and 120
The least common multiple (LCM) of 75 and 120 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 75 and 120?
First, calculate the GCD of 75 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 120 = 0 remainder 75 |
| 2 | 120 ÷ 75 = 1 remainder 45 |
| 3 | 75 ÷ 45 = 1 remainder 30 |
| 4 | 45 ÷ 30 = 1 remainder 15 |
| 5 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 101 | 13635 |
| 160 and 144 | 1440 |
| 107 and 32 | 3424 |
| 65 and 50 | 650 |
| 83 and 120 | 9960 |