Least Common Multiple (LCM) of 100 and 13
The least common multiple (LCM) of 100 and 13 is 1300.
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 13?
First, calculate the GCD of 100 and 13 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 13 = 7 remainder 9 |
| 2 | 13 ÷ 9 = 1 remainder 4 |
| 3 | 9 ÷ 4 = 2 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 153 | 3366 |
| 62 and 114 | 3534 |
| 175 and 182 | 4550 |
| 133 and 37 | 4921 |
| 158 and 25 | 3950 |