Least Common Multiple (LCM) of 157 and 99
The least common multiple (LCM) of 157 and 99 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 157 and 99?
First, calculate the GCD of 157 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 99 = 1 remainder 58 |
| 2 | 99 ÷ 58 = 1 remainder 41 |
| 3 | 58 ÷ 41 = 1 remainder 17 |
| 4 | 41 ÷ 17 = 2 remainder 7 |
| 5 | 17 ÷ 7 = 2 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 95 | 17005 |
| 168 and 44 | 1848 |
| 118 and 128 | 7552 |
| 131 and 117 | 15327 |
| 131 and 75 | 9825 |