Least Common Multiple (LCM) of 99 and 158
The least common multiple (LCM) of 99 and 158 is 15642.
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 158?
First, calculate the GCD of 99 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 158 = 0 remainder 99 |
| 2 | 158 ÷ 99 = 1 remainder 59 |
| 3 | 99 ÷ 59 = 1 remainder 40 |
| 4 | 59 ÷ 40 = 1 remainder 19 |
| 5 | 40 ÷ 19 = 2 remainder 2 |
| 6 | 19 ÷ 2 = 9 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 57 | 2109 |
| 116 and 180 | 5220 |
| 101 and 11 | 1111 |
| 164 and 103 | 16892 |
| 54 and 67 | 3618 |