Least Common Multiple (LCM) of 113 and 27
The least common multiple (LCM) of 113 and 27 is 3051.
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 27?
First, calculate the GCD of 113 and 27 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 27 = 4 remainder 5 |
| 2 | 27 ÷ 5 = 5 remainder 2 |
| 3 | 5 ÷ 2 = 2 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 50 | 4950 |
| 61 and 27 | 1647 |
| 98 and 173 | 16954 |
| 38 and 53 | 2014 |
| 95 and 80 | 1520 |