Least Common Multiple (LCM) of 150 and 45
The least common multiple (LCM) of 150 and 45 is 450.
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 150 and 45?
First, calculate the GCD of 150 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 45 = 3 remainder 15 |
| 2 | 45 ÷ 15 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 102 | 6630 |
| 12 and 89 | 1068 |
| 76 and 107 | 8132 |
| 51 and 13 | 663 |
| 135 and 69 | 3105 |