Least Common Multiple (LCM) of 100 and 56
The least common multiple (LCM) of 100 and 56 is 1400.
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 100 and 56?
First, calculate the GCD of 100 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 56 = 1 remainder 44 |
| 2 | 56 ÷ 44 = 1 remainder 12 |
| 3 | 44 ÷ 12 = 3 remainder 8 |
| 4 | 12 ÷ 8 = 1 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 100 | 10100 |
| 15 and 62 | 930 |
| 12 and 93 | 372 |
| 146 and 89 | 12994 |
| 105 and 31 | 3255 |