Least Common Multiple (LCM) of 60 and 53
The least common multiple (LCM) of 60 and 53 is 3180.
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 60 and 53?
First, calculate the GCD of 60 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 53 = 1 remainder 7 |
| 2 | 53 ÷ 7 = 7 remainder 4 |
| 3 | 7 ÷ 4 = 1 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 118 | 7316 |
| 139 and 23 | 3197 |
| 16 and 23 | 368 |
| 59 and 85 | 5015 |
| 106 and 137 | 14522 |