Least Common Multiple (LCM) of 60 and 76
The least common multiple (LCM) of 60 and 76 is 1140.
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 76?
First, calculate the GCD of 60 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 76 = 0 remainder 60 |
| 2 | 76 ÷ 60 = 1 remainder 16 |
| 3 | 60 ÷ 16 = 3 remainder 12 |
| 4 | 16 ÷ 12 = 1 remainder 4 |
| 5 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 123 | 984 |
| 21 and 111 | 777 |
| 132 and 41 | 5412 |
| 89 and 129 | 11481 |
| 125 and 189 | 23625 |