Least Common Multiple (LCM) of 37 and 72
The least common multiple (LCM) of 37 and 72 is 2664.
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 72?
First, calculate the GCD of 37 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 72 = 0 remainder 37 |
| 2 | 72 ÷ 37 = 1 remainder 35 |
| 3 | 37 ÷ 35 = 1 remainder 2 |
| 4 | 35 ÷ 2 = 17 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 127 | 12573 |
| 95 and 70 | 1330 |
| 163 and 172 | 28036 |
| 46 and 11 | 506 |
| 90 and 198 | 990 |