Least Common Multiple (LCM) of 105 and 53
The least common multiple (LCM) of 105 and 53 is 5565.
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 105 and 53?
First, calculate the GCD of 105 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 53 = 1 remainder 52 |
| 2 | 53 ÷ 52 = 1 remainder 1 |
| 3 | 52 ÷ 1 = 52 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 57 | 342 |
| 52 and 80 | 1040 |
| 85 and 145 | 2465 |
| 159 and 198 | 10494 |
| 112 and 117 | 13104 |