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 |
|---|---|
| 143 and 71 | 10153 |
| 108 and 185 | 19980 |
| 36 and 136 | 1224 |
| 96 and 157 | 15072 |
| 45 and 100 | 900 |