Least Common Multiple (LCM) of 40 and 62
The least common multiple (LCM) of 40 and 62 is 1240.
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 62?
First, calculate the GCD of 40 and 62 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 62 = 0 remainder 40 |
| 2 | 62 ÷ 40 = 1 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 |
|---|---|
| 74 and 73 | 5402 |
| 78 and 13 | 78 |
| 147 and 112 | 2352 |
| 165 and 82 | 13530 |
| 152 and 111 | 16872 |