Least Common Multiple (LCM) of 64 and 175
The least common multiple (LCM) of 64 and 175 is 11200.
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 175?
First, calculate the GCD of 64 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 175 = 0 remainder 64 |
| 2 | 175 ÷ 64 = 2 remainder 47 |
| 3 | 64 ÷ 47 = 1 remainder 17 |
| 4 | 47 ÷ 17 = 2 remainder 13 |
| 5 | 17 ÷ 13 = 1 remainder 4 |
| 6 | 13 ÷ 4 = 3 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 120 | 21480 |
| 179 and 164 | 29356 |
| 73 and 143 | 10439 |
| 24 and 189 | 1512 |
| 31 and 137 | 4247 |