Least Common Multiple (LCM) of 96 and 157
The least common multiple (LCM) of 96 and 157 is 15072.
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 96 and 157?
First, calculate the GCD of 96 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 157 = 0 remainder 96 |
| 2 | 157 ÷ 96 = 1 remainder 61 |
| 3 | 96 ÷ 61 = 1 remainder 35 |
| 4 | 61 ÷ 35 = 1 remainder 26 |
| 5 | 35 ÷ 26 = 1 remainder 9 |
| 6 | 26 ÷ 9 = 2 remainder 8 |
| 7 | 9 ÷ 8 = 1 remainder 1 |
| 8 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 86 | 2236 |
| 184 and 110 | 10120 |
| 132 and 108 | 1188 |
| 149 and 58 | 8642 |
| 38 and 199 | 7562 |