Least Common Multiple (LCM) of 40 and 115
The least common multiple (LCM) of 40 and 115 is 920.
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 115?
First, calculate the GCD of 40 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 115 = 0 remainder 40 |
| 2 | 115 ÷ 40 = 2 remainder 35 |
| 3 | 40 ÷ 35 = 1 remainder 5 |
| 4 | 35 ÷ 5 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 105 | 17115 |
| 138 and 108 | 2484 |
| 13 and 148 | 1924 |
| 126 and 85 | 10710 |
| 189 and 21 | 189 |