Least Common Multiple (LCM) of 40 and 157
The least common multiple (LCM) of 40 and 157 is 6280.
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 157?
First, calculate the GCD of 40 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 157 = 0 remainder 40 |
| 2 | 157 ÷ 40 = 3 remainder 37 |
| 3 | 40 ÷ 37 = 1 remainder 3 |
| 4 | 37 ÷ 3 = 12 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 189 | 3591 |
| 33 and 47 | 1551 |
| 116 and 146 | 8468 |
| 60 and 110 | 660 |
| 72 and 122 | 4392 |