Least Common Multiple (LCM) of 40 and 91
The least common multiple (LCM) of 40 and 91 is 3640.
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 91?
First, calculate the GCD of 40 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 91 = 0 remainder 40 |
| 2 | 91 ÷ 40 = 2 remainder 11 |
| 3 | 40 ÷ 11 = 3 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 143 | 143 |
| 192 and 184 | 4416 |
| 172 and 75 | 12900 |
| 118 and 142 | 8378 |
| 106 and 33 | 3498 |