Least Common Multiple (LCM) of 100 and 51
The least common multiple (LCM) of 100 and 51 is 5100.
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 51?
First, calculate the GCD of 100 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 51 = 1 remainder 49 |
| 2 | 51 ÷ 49 = 1 remainder 2 |
| 3 | 49 ÷ 2 = 24 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 72 | 5256 |
| 75 and 30 | 150 |
| 167 and 22 | 3674 |
| 199 and 56 | 11144 |
| 158 and 198 | 15642 |