Least Common Multiple (LCM) of 54 and 150
The least common multiple (LCM) of 54 and 150 is 1350.
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 54 and 150?
First, calculate the GCD of 54 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 150 = 0 remainder 54 |
| 2 | 150 ÷ 54 = 2 remainder 42 |
| 3 | 54 ÷ 42 = 1 remainder 12 |
| 4 | 42 ÷ 12 = 3 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 78 | 7644 |
| 89 and 166 | 14774 |
| 82 and 11 | 902 |
| 166 and 53 | 8798 |
| 75 and 103 | 7725 |