Least Common Multiple (LCM) of 53 and 100
The least common multiple (LCM) of 53 and 100 is 5300.
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 53 and 100?
First, calculate the GCD of 53 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 100 = 0 remainder 53 |
| 2 | 100 ÷ 53 = 1 remainder 47 |
| 3 | 53 ÷ 47 = 1 remainder 6 |
| 4 | 47 ÷ 6 = 7 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 186 | 15810 |
| 156 and 182 | 1092 |
| 39 and 138 | 1794 |
| 38 and 68 | 1292 |
| 105 and 77 | 1155 |