Least Common Multiple (LCM) of 64 and 157
The least common multiple (LCM) of 64 and 157 is 10048.
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 157?
First, calculate the GCD of 64 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 157 = 0 remainder 64 |
| 2 | 157 ÷ 64 = 2 remainder 29 |
| 3 | 64 ÷ 29 = 2 remainder 6 |
| 4 | 29 ÷ 6 = 4 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 45 | 90 |
| 71 and 111 | 7881 |
| 188 and 197 | 37036 |
| 28 and 46 | 644 |
| 146 and 131 | 19126 |