Least Common Multiple (LCM) of 40 and 49
The least common multiple (LCM) of 40 and 49 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 40 and 49?
First, calculate the GCD of 40 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 49 = 0 remainder 40 |
| 2 | 49 ÷ 40 = 1 remainder 9 |
| 3 | 40 ÷ 9 = 4 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 166 | 27722 |
| 46 and 48 | 1104 |
| 80 and 125 | 2000 |
| 54 and 78 | 702 |
| 162 and 134 | 10854 |