Least Common Multiple (LCM) of 64 and 77
The least common multiple (LCM) of 64 and 77 is 4928.
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 64 and 77?
First, calculate the GCD of 64 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 77 = 0 remainder 64 |
| 2 | 77 ÷ 64 = 1 remainder 13 |
| 3 | 64 ÷ 13 = 4 remainder 12 |
| 4 | 13 ÷ 12 = 1 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 106 | 13038 |
| 160 and 145 | 4640 |
| 39 and 120 | 1560 |
| 118 and 67 | 7906 |
| 146 and 43 | 6278 |