Least Common Multiple (LCM) of 117 and 64
The least common multiple (LCM) of 117 and 64 is 7488.
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 117 and 64?
First, calculate the GCD of 117 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 64 = 1 remainder 53 |
| 2 | 64 ÷ 53 = 1 remainder 11 |
| 3 | 53 ÷ 11 = 4 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 27 | 2889 |
| 125 and 54 | 6750 |
| 140 and 113 | 15820 |
| 131 and 125 | 16375 |
| 196 and 82 | 8036 |