Least Common Multiple (LCM) of 64 and 116
The least common multiple (LCM) of 64 and 116 is 1856.
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 116?
First, calculate the GCD of 64 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 116 = 0 remainder 64 |
| 2 | 116 ÷ 64 = 1 remainder 52 |
| 3 | 64 ÷ 52 = 1 remainder 12 |
| 4 | 52 ÷ 12 = 4 remainder 4 |
| 5 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 12 | 852 |
| 145 and 173 | 25085 |
| 115 and 169 | 19435 |
| 144 and 48 | 144 |
| 37 and 74 | 74 |