Least Common Multiple (LCM) of 37 and 60
The least common multiple (LCM) of 37 and 60 is 2220.
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 60?
First, calculate the GCD of 37 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 60 = 0 remainder 37 |
| 2 | 60 ÷ 37 = 1 remainder 23 |
| 3 | 37 ÷ 23 = 1 remainder 14 |
| 4 | 23 ÷ 14 = 1 remainder 9 |
| 5 | 14 ÷ 9 = 1 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 13 | 1443 |
| 77 and 198 | 1386 |
| 123 and 71 | 8733 |
| 10 and 12 | 60 |
| 155 and 16 | 2480 |