Least Common Multiple (LCM) of 64 and 168
The least common multiple (LCM) of 64 and 168 is 1344.
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 168?
First, calculate the GCD of 64 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 168 = 0 remainder 64 |
| 2 | 168 ÷ 64 = 2 remainder 40 |
| 3 | 64 ÷ 40 = 1 remainder 24 |
| 4 | 40 ÷ 24 = 1 remainder 16 |
| 5 | 24 ÷ 16 = 1 remainder 8 |
| 6 | 16 ÷ 8 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 85 | 14195 |
| 48 and 118 | 2832 |
| 85 and 172 | 14620 |
| 136 and 100 | 3400 |
| 107 and 102 | 10914 |