Least Common Multiple (LCM) of 109 and 53
The least common multiple (LCM) of 109 and 53 is 5777.
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 109 and 53?
First, calculate the GCD of 109 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 53 = 2 remainder 3 |
| 2 | 53 ÷ 3 = 17 remainder 2 |
| 3 | 3 ÷ 2 = 1 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 128 | 9344 |
| 89 and 162 | 14418 |
| 53 and 110 | 5830 |
| 111 and 86 | 9546 |
| 132 and 123 | 5412 |