Least Common Multiple (LCM) of 60 and 150
The least common multiple (LCM) of 60 and 150 is 300.
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 60 and 150?
First, calculate the GCD of 60 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 150 = 0 remainder 60 |
| 2 | 150 ÷ 60 = 2 remainder 30 |
| 3 | 60 ÷ 30 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 84 | 15540 |
| 65 and 44 | 2860 |
| 126 and 60 | 1260 |
| 105 and 23 | 2415 |
| 147 and 117 | 5733 |