Least Common Multiple (LCM) of 157 and 96
The least common multiple (LCM) of 157 and 96 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 157 and 96?
First, calculate the GCD of 157 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 96 = 1 remainder 61 |
| 2 | 96 ÷ 61 = 1 remainder 35 |
| 3 | 61 ÷ 35 = 1 remainder 26 |
| 4 | 35 ÷ 26 = 1 remainder 9 |
| 5 | 26 ÷ 9 = 2 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 75 | 2100 |
| 198 and 40 | 3960 |
| 79 and 67 | 5293 |
| 114 and 106 | 6042 |
| 159 and 198 | 10494 |