Least Common Multiple (LCM) of 113 and 106
The least common multiple (LCM) of 113 and 106 is 11978.
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 113 and 106?
First, calculate the GCD of 113 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 106 = 1 remainder 7 |
| 2 | 106 ÷ 7 = 15 remainder 1 |
| 3 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 61 | 7869 |
| 45 and 127 | 5715 |
| 63 and 125 | 7875 |
| 119 and 88 | 10472 |
| 135 and 69 | 3105 |