Least Common Multiple (LCM) of 53 and 111
The least common multiple (LCM) of 53 and 111 is 5883.
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 111?
First, calculate the GCD of 53 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 111 = 0 remainder 53 |
| 2 | 111 ÷ 53 = 2 remainder 5 |
| 3 | 53 ÷ 5 = 10 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 88 | 14168 |
| 58 and 98 | 2842 |
| 163 and 11 | 1793 |
| 145 and 29 | 145 |
| 159 and 182 | 28938 |