Least Common Multiple (LCM) of 40 and 114
The least common multiple (LCM) of 40 and 114 is 2280.
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 114?
First, calculate the GCD of 40 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 114 = 0 remainder 40 |
| 2 | 114 ÷ 40 = 2 remainder 34 |
| 3 | 40 ÷ 34 = 1 remainder 6 |
| 4 | 34 ÷ 6 = 5 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 135 | 1080 |
| 153 and 56 | 8568 |
| 170 and 139 | 23630 |
| 48 and 135 | 2160 |
| 167 and 99 | 16533 |