Least Common Multiple (LCM) of 150 and 65
The least common multiple (LCM) of 150 and 65 is 1950.
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 65?
First, calculate the GCD of 150 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 65 = 2 remainder 20 |
| 2 | 65 ÷ 20 = 3 remainder 5 |
| 3 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 162 | 1134 |
| 154 and 111 | 17094 |
| 31 and 115 | 3565 |
| 57 and 67 | 3819 |
| 107 and 31 | 3317 |