Least Common Multiple (LCM) of 67 and 113
The least common multiple (LCM) of 67 and 113 is 7571.
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 113?
First, calculate the GCD of 67 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 113 = 0 remainder 67 |
| 2 | 113 ÷ 67 = 1 remainder 46 |
| 3 | 67 ÷ 46 = 1 remainder 21 |
| 4 | 46 ÷ 21 = 2 remainder 4 |
| 5 | 21 ÷ 4 = 5 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 37 | 5957 |
| 148 and 53 | 7844 |
| 144 and 31 | 4464 |
| 160 and 82 | 6560 |
| 134 and 123 | 16482 |