Least Common Multiple (LCM) of 40 and 61
The least common multiple (LCM) of 40 and 61 is 2440.
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 61?
First, calculate the GCD of 40 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 61 = 0 remainder 40 |
| 2 | 61 ÷ 40 = 1 remainder 21 |
| 3 | 40 ÷ 21 = 1 remainder 19 |
| 4 | 21 ÷ 19 = 1 remainder 2 |
| 5 | 19 ÷ 2 = 9 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 29 | 4466 |
| 141 and 171 | 8037 |
| 181 and 65 | 11765 |
| 33 and 44 | 132 |
| 169 and 185 | 31265 |