Least Common Multiple (LCM) of 53 and 134
The least common multiple (LCM) of 53 and 134 is 7102.
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 134?
First, calculate the GCD of 53 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 134 = 0 remainder 53 |
| 2 | 134 ÷ 53 = 2 remainder 28 |
| 3 | 53 ÷ 28 = 1 remainder 25 |
| 4 | 28 ÷ 25 = 1 remainder 3 |
| 5 | 25 ÷ 3 = 8 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 19 | 3230 |
| 105 and 136 | 14280 |
| 153 and 31 | 4743 |
| 86 and 182 | 7826 |
| 175 and 178 | 31150 |