Least Common Multiple (LCM) of 40 and 113
The least common multiple (LCM) of 40 and 113 is 4520.
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 40 and 113?
First, calculate the GCD of 40 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 113 = 0 remainder 40 |
| 2 | 113 ÷ 40 = 2 remainder 33 |
| 3 | 40 ÷ 33 = 1 remainder 7 |
| 4 | 33 ÷ 7 = 4 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 147 | 16170 |
| 22 and 185 | 4070 |
| 175 and 196 | 4900 |
| 129 and 196 | 25284 |
| 151 and 115 | 17365 |