Least Common Multiple (LCM) of 64 and 172
The least common multiple (LCM) of 64 and 172 is 2752.
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 172?
First, calculate the GCD of 64 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 172 = 0 remainder 64 |
| 2 | 172 ÷ 64 = 2 remainder 44 |
| 3 | 64 ÷ 44 = 1 remainder 20 |
| 4 | 44 ÷ 20 = 2 remainder 4 |
| 5 | 20 ÷ 4 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 59 | 5664 |
| 165 and 148 | 24420 |
| 31 and 155 | 155 |
| 113 and 170 | 19210 |
| 25 and 147 | 3675 |