Least Common Multiple (LCM) of 113 and 39
The least common multiple (LCM) of 113 and 39 is 4407.
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 39?
First, calculate the GCD of 113 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 39 = 2 remainder 35 |
| 2 | 39 ÷ 35 = 1 remainder 4 |
| 3 | 35 ÷ 4 = 8 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 140 | 7420 |
| 63 and 25 | 1575 |
| 165 and 58 | 9570 |
| 115 and 40 | 920 |
| 112 and 170 | 9520 |