Least Common Multiple (LCM) of 123 and 158
The least common multiple (LCM) of 123 and 158 is 19434.
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 123 and 158?
First, calculate the GCD of 123 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 158 = 0 remainder 123 |
| 2 | 158 ÷ 123 = 1 remainder 35 |
| 3 | 123 ÷ 35 = 3 remainder 18 |
| 4 | 35 ÷ 18 = 1 remainder 17 |
| 5 | 18 ÷ 17 = 1 remainder 1 |
| 6 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 80 | 4240 |
| 148 and 77 | 11396 |
| 116 and 66 | 3828 |
| 172 and 57 | 9804 |
| 78 and 118 | 4602 |