Least Common Multiple (LCM) of 150 and 96
The least common multiple (LCM) of 150 and 96 is 2400.
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 96?
First, calculate the GCD of 150 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 96 = 1 remainder 54 |
| 2 | 96 ÷ 54 = 1 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 |
|---|---|
| 37 and 136 | 5032 |
| 84 and 87 | 2436 |
| 77 and 72 | 5544 |
| 78 and 97 | 7566 |
| 32 and 186 | 2976 |