Least Common Multiple (LCM) of 120 and 150
The least common multiple (LCM) of 120 and 150 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 150?
First, calculate the GCD of 120 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 150 = 0 remainder 120 |
| 2 | 150 ÷ 120 = 1 remainder 30 |
| 3 | 120 ÷ 30 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 152 | 2280 |
| 127 and 135 | 17145 |
| 107 and 77 | 8239 |
| 142 and 91 | 12922 |
| 153 and 106 | 16218 |