Least Common Multiple (LCM) of 100 and 52
The least common multiple (LCM) of 100 and 52 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 52?
First, calculate the GCD of 100 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 52 = 1 remainder 48 |
| 2 | 52 ÷ 48 = 1 remainder 4 |
| 3 | 48 ÷ 4 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 104 | 10088 |
| 49 and 136 | 6664 |
| 35 and 198 | 6930 |
| 176 and 155 | 27280 |
| 149 and 111 | 16539 |