Least Common Multiple (LCM) of 64 and 167
The least common multiple (LCM) of 64 and 167 is 10688.
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 167?
First, calculate the GCD of 64 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 167 = 0 remainder 64 |
| 2 | 167 ÷ 64 = 2 remainder 39 |
| 3 | 64 ÷ 39 = 1 remainder 25 |
| 4 | 39 ÷ 25 = 1 remainder 14 |
| 5 | 25 ÷ 14 = 1 remainder 11 |
| 6 | 14 ÷ 11 = 1 remainder 3 |
| 7 | 11 ÷ 3 = 3 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 40 | 280 |
| 29 and 176 | 5104 |
| 149 and 30 | 4470 |
| 63 and 30 | 630 |
| 21 and 50 | 1050 |