Least Common Multiple (LCM) of 67 and 53
The least common multiple (LCM) of 67 and 53 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 67 and 53?
First, calculate the GCD of 67 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 53 = 1 remainder 14 |
| 2 | 53 ÷ 14 = 3 remainder 11 |
| 3 | 14 ÷ 11 = 1 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 36 | 288 |
| 129 and 196 | 25284 |
| 28 and 137 | 3836 |
| 37 and 102 | 3774 |
| 153 and 134 | 20502 |