Least Common Multiple (LCM) of 12 and 40
The least common multiple (LCM) of 12 and 40 is 120.
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 12 and 40?
First, calculate the GCD of 12 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 40 = 0 remainder 12 |
| 2 | 40 ÷ 12 = 3 remainder 4 |
| 3 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 62 | 3348 |
| 123 and 96 | 3936 |
| 82 and 61 | 5002 |
| 157 and 103 | 16171 |
| 17 and 116 | 1972 |