Least Common Multiple (LCM) of 106 and 113
The least common multiple (LCM) of 106 and 113 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 106 and 113?
First, calculate the GCD of 106 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 113 = 0 remainder 106 |
| 2 | 113 ÷ 106 = 1 remainder 7 |
| 3 | 106 ÷ 7 = 15 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 178 | 8722 |
| 31 and 138 | 4278 |
| 63 and 87 | 1827 |
| 103 and 199 | 20497 |
| 105 and 182 | 2730 |