Least Common Multiple (LCM) of 64 and 117
The least common multiple (LCM) of 64 and 117 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 64 and 117?
First, calculate the GCD of 64 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 117 = 0 remainder 64 |
| 2 | 117 ÷ 64 = 1 remainder 53 |
| 3 | 64 ÷ 53 = 1 remainder 11 |
| 4 | 53 ÷ 11 = 4 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 98 | 98 |
| 99 and 187 | 1683 |
| 177 and 30 | 1770 |
| 173 and 191 | 33043 |
| 78 and 152 | 5928 |