Least Common Multiple (LCM) of 40 and 142
The least common multiple (LCM) of 40 and 142 is 2840.
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 142?
First, calculate the GCD of 40 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 142 = 0 remainder 40 |
| 2 | 142 ÷ 40 = 3 remainder 22 |
| 3 | 40 ÷ 22 = 1 remainder 18 |
| 4 | 22 ÷ 18 = 1 remainder 4 |
| 5 | 18 ÷ 4 = 4 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 11 | 1980 |
| 70 and 39 | 2730 |
| 14 and 179 | 2506 |
| 160 and 135 | 4320 |
| 165 and 96 | 5280 |