Least Common Multiple (LCM) of 40 and 76
The least common multiple (LCM) of 40 and 76 is 760.
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 76?
First, calculate the GCD of 40 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 76 = 0 remainder 40 |
| 2 | 76 ÷ 40 = 1 remainder 36 |
| 3 | 40 ÷ 36 = 1 remainder 4 |
| 4 | 36 ÷ 4 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 26 and 123 | 3198 |
| 125 and 192 | 24000 |
| 120 and 139 | 16680 |
| 164 and 16 | 656 |
| 116 and 13 | 1508 |