Least Common Multiple (LCM) of 60 and 77
The least common multiple (LCM) of 60 and 77 is 4620.
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 77?
First, calculate the GCD of 60 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 77 = 0 remainder 60 |
| 2 | 77 ÷ 60 = 1 remainder 17 |
| 3 | 60 ÷ 17 = 3 remainder 9 |
| 4 | 17 ÷ 9 = 1 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 172 | 18060 |
| 76 and 97 | 7372 |
| 58 and 128 | 3712 |
| 127 and 165 | 20955 |
| 101 and 167 | 16867 |