Least Common Multiple (LCM) of 96 and 150
The least common multiple (LCM) of 96 and 150 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 96 and 150?
First, calculate the GCD of 96 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 150 = 0 remainder 96 |
| 2 | 150 ÷ 96 = 1 remainder 54 |
| 3 | 96 ÷ 54 = 1 remainder 42 |
| 4 | 54 ÷ 42 = 1 remainder 12 |
| 5 | 42 ÷ 12 = 3 remainder 6 |
| 6 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 114 | 3078 |
| 150 and 136 | 10200 |
| 24 and 177 | 1416 |
| 92 and 180 | 4140 |
| 151 and 57 | 8607 |