Least Common Multiple (LCM) of 64 and 178
The least common multiple (LCM) of 64 and 178 is 5696.
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 178?
First, calculate the GCD of 64 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 178 = 0 remainder 64 |
| 2 | 178 ÷ 64 = 2 remainder 50 |
| 3 | 64 ÷ 50 = 1 remainder 14 |
| 4 | 50 ÷ 14 = 3 remainder 8 |
| 5 | 14 ÷ 8 = 1 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 134 | 10988 |
| 42 and 48 | 336 |
| 191 and 36 | 6876 |
| 178 and 41 | 7298 |
| 82 and 67 | 5494 |