Least Common Multiple (LCM) of 37 and 75
The least common multiple (LCM) of 37 and 75 is 2775.
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 37 and 75?
First, calculate the GCD of 37 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 75 = 0 remainder 37 |
| 2 | 75 ÷ 37 = 2 remainder 1 |
| 3 | 37 ÷ 1 = 37 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 132 | 264 |
| 52 and 105 | 5460 |
| 133 and 90 | 11970 |
| 76 and 175 | 13300 |
| 71 and 71 | 71 |