Least Common Multiple (LCM) of 40 and 102
The least common multiple (LCM) of 40 and 102 is 2040.
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 102?
First, calculate the GCD of 40 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 102 = 0 remainder 40 |
| 2 | 102 ÷ 40 = 2 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 |
|---|---|
| 136 and 175 | 23800 |
| 200 and 91 | 18200 |
| 196 and 138 | 13524 |
| 70 and 131 | 9170 |
| 182 and 131 | 23842 |