Least Common Multiple (LCM) of 126 and 113
The least common multiple (LCM) of 126 and 113 is 14238.
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 126 and 113?
First, calculate the GCD of 126 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 113 = 1 remainder 13 |
| 2 | 113 ÷ 13 = 8 remainder 9 |
| 3 | 13 ÷ 9 = 1 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 106 | 3498 |
| 166 and 135 | 22410 |
| 178 and 35 | 6230 |
| 152 and 153 | 23256 |
| 18 and 119 | 2142 |