Least Common Multiple (LCM) of 40 and 53
The least common multiple (LCM) of 40 and 53 is 2120.
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 53?
First, calculate the GCD of 40 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 53 = 0 remainder 40 |
| 2 | 53 ÷ 40 = 1 remainder 13 |
| 3 | 40 ÷ 13 = 3 remainder 1 |
| 4 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 100 | 3700 |
| 189 and 108 | 756 |
| 146 and 139 | 20294 |
| 120 and 173 | 20760 |
| 35 and 64 | 2240 |