Least Common Multiple (LCM) of 67 and 46
The least common multiple (LCM) of 67 and 46 is 3082.
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 46?
First, calculate the GCD of 67 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 46 = 1 remainder 21 |
| 2 | 46 ÷ 21 = 2 remainder 4 |
| 3 | 21 ÷ 4 = 5 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 103 | 8240 |
| 130 and 179 | 23270 |
| 79 and 130 | 10270 |
| 22 and 119 | 2618 |
| 149 and 65 | 9685 |