Least Common Multiple (LCM) of 52 and 100
The least common multiple (LCM) of 52 and 100 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 52 and 100?
First, calculate the GCD of 52 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 100 = 0 remainder 52 |
| 2 | 100 ÷ 52 = 1 remainder 48 |
| 3 | 52 ÷ 48 = 1 remainder 4 |
| 4 | 48 ÷ 4 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 200 | 5800 |
| 96 and 181 | 17376 |
| 74 and 176 | 6512 |
| 152 and 103 | 15656 |
| 17 and 40 | 680 |