Least Common Multiple (LCM) of 150 and 76
The least common multiple (LCM) of 150 and 76 is 5700.
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 76?
First, calculate the GCD of 150 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 76 = 1 remainder 74 |
| 2 | 76 ÷ 74 = 1 remainder 2 |
| 3 | 74 ÷ 2 = 37 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 137 | 14385 |
| 85 and 45 | 765 |
| 96 and 186 | 2976 |
| 54 and 154 | 4158 |
| 162 and 149 | 24138 |