Least Common Multiple (LCM) of 37 and 105
The least common multiple (LCM) of 37 and 105 is 3885.
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 105?
First, calculate the GCD of 37 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 105 = 0 remainder 37 |
| 2 | 105 ÷ 37 = 2 remainder 31 |
| 3 | 37 ÷ 31 = 1 remainder 6 |
| 4 | 31 ÷ 6 = 5 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 79 | 1817 |
| 104 and 36 | 936 |
| 100 and 71 | 7100 |
| 64 and 199 | 12736 |
| 178 and 101 | 17978 |