Least Common Multiple (LCM) of 37 and 102
The least common multiple (LCM) of 37 and 102 is 3774.
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 102?
First, calculate the GCD of 37 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 102 = 0 remainder 37 |
| 2 | 102 ÷ 37 = 2 remainder 28 |
| 3 | 37 ÷ 28 = 1 remainder 9 |
| 4 | 28 ÷ 9 = 3 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 106 | 11766 |
| 192 and 175 | 33600 |
| 31 and 89 | 2759 |
| 127 and 12 | 1524 |
| 69 and 198 | 4554 |