Least Common Multiple (LCM) of 40 and 55
The least common multiple (LCM) of 40 and 55 is 440.
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 55?
First, calculate the GCD of 40 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 55 = 0 remainder 40 |
| 2 | 55 ÷ 40 = 1 remainder 15 |
| 3 | 40 ÷ 15 = 2 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 175 | 525 |
| 65 and 55 | 715 |
| 108 and 158 | 8532 |
| 151 and 178 | 26878 |
| 70 and 108 | 3780 |