Least Common Multiple (LCM) of 100 and 133
The least common multiple (LCM) of 100 and 133 is 13300.
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 133?
First, calculate the GCD of 100 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 133 = 0 remainder 100 |
| 2 | 133 ÷ 100 = 1 remainder 33 |
| 3 | 100 ÷ 33 = 3 remainder 1 |
| 4 | 33 ÷ 1 = 33 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 67 | 7303 |
| 172 and 178 | 15308 |
| 177 and 107 | 18939 |
| 108 and 148 | 3996 |
| 51 and 56 | 2856 |