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 |
|---|---|
| 106 and 76 | 4028 |
| 92 and 17 | 1564 |
| 71 and 172 | 12212 |
| 11 and 167 | 1837 |
| 107 and 35 | 3745 |