Least Common Multiple (LCM) of 99 and 157
The least common multiple (LCM) of 99 and 157 is 15543.
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 99 and 157?
First, calculate the GCD of 99 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 157 = 0 remainder 99 |
| 2 | 157 ÷ 99 = 1 remainder 58 |
| 3 | 99 ÷ 58 = 1 remainder 41 |
| 4 | 58 ÷ 41 = 1 remainder 17 |
| 5 | 41 ÷ 17 = 2 remainder 7 |
| 6 | 17 ÷ 7 = 2 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 140 | 5740 |
| 165 and 29 | 4785 |
| 152 and 42 | 3192 |
| 76 and 25 | 1900 |
| 149 and 158 | 23542 |