Least Common Multiple (LCM) of 40 and 116
The least common multiple (LCM) of 40 and 116 is 1160.
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 116?
First, calculate the GCD of 40 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 116 = 0 remainder 40 |
| 2 | 116 ÷ 40 = 2 remainder 36 |
| 3 | 40 ÷ 36 = 1 remainder 4 |
| 4 | 36 ÷ 4 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 167 | 24048 |
| 124 and 153 | 18972 |
| 118 and 123 | 14514 |
| 150 and 156 | 3900 |
| 172 and 87 | 14964 |