Least Common Multiple (LCM) of 40 and 97
The least common multiple (LCM) of 40 and 97 is 3880.
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 97?
First, calculate the GCD of 40 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 97 = 0 remainder 40 |
| 2 | 97 ÷ 40 = 2 remainder 17 |
| 3 | 40 ÷ 17 = 2 remainder 6 |
| 4 | 17 ÷ 6 = 2 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 49 | 7595 |
| 190 and 121 | 22990 |
| 53 and 70 | 3710 |
| 69 and 142 | 9798 |
| 74 and 110 | 4070 |