Least Common Multiple (LCM) of 53 and 114
The least common multiple (LCM) of 53 and 114 is 6042.
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 114?
First, calculate the GCD of 53 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 114 = 0 remainder 53 |
| 2 | 114 ÷ 53 = 2 remainder 8 |
| 3 | 53 ÷ 8 = 6 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 26 | 1898 |
| 110 and 119 | 13090 |
| 183 and 79 | 14457 |
| 15 and 96 | 480 |
| 62 and 11 | 682 |