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 |
|---|---|
| 28 and 15 | 420 |
| 116 and 150 | 8700 |
| 126 and 176 | 11088 |
| 135 and 64 | 8640 |
| 27 and 157 | 4239 |