Least Common Multiple (LCM) of 76 and 150
The least common multiple (LCM) of 76 and 150 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 76 and 150?
First, calculate the GCD of 76 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 150 = 0 remainder 76 |
| 2 | 150 ÷ 76 = 1 remainder 74 |
| 3 | 76 ÷ 74 = 1 remainder 2 |
| 4 | 74 ÷ 2 = 37 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 105 | 210 |
| 30 and 195 | 390 |
| 180 and 177 | 10620 |
| 17 and 104 | 1768 |
| 129 and 59 | 7611 |