Least Common Multiple (LCM) of 49 and 40
The least common multiple (LCM) of 49 and 40 is 1960.
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 49 and 40?
First, calculate the GCD of 49 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 40 = 1 remainder 9 |
| 2 | 40 ÷ 9 = 4 remainder 4 |
| 3 | 9 ÷ 4 = 2 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 135 | 945 |
| 135 and 10 | 270 |
| 40 and 46 | 920 |
| 199 and 183 | 36417 |
| 178 and 167 | 29726 |