Least Common Multiple (LCM) of 40 and 101
The least common multiple (LCM) of 40 and 101 is 4040.
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 101?
First, calculate the GCD of 40 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 101 = 0 remainder 40 |
| 2 | 101 ÷ 40 = 2 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 |
|---|---|
| 105 and 123 | 4305 |
| 167 and 57 | 9519 |
| 165 and 194 | 32010 |
| 130 and 102 | 6630 |
| 40 and 118 | 2360 |