Least Common Multiple (LCM) of 53 and 67
The least common multiple (LCM) of 53 and 67 is 3551.
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 67?
First, calculate the GCD of 53 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 67 = 0 remainder 53 |
| 2 | 67 ÷ 53 = 1 remainder 14 |
| 3 | 53 ÷ 14 = 3 remainder 11 |
| 4 | 14 ÷ 11 = 1 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 157 | 4867 |
| 154 and 19 | 2926 |
| 115 and 95 | 2185 |
| 166 and 120 | 9960 |
| 114 and 153 | 5814 |