Least Common Multiple (LCM) of 67 and 47
The least common multiple (LCM) of 67 and 47 is 3149.
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 47?
First, calculate the GCD of 67 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 47 = 1 remainder 20 |
| 2 | 47 ÷ 20 = 2 remainder 7 |
| 3 | 20 ÷ 7 = 2 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 123 | 6765 |
| 114 and 31 | 3534 |
| 199 and 107 | 21293 |
| 140 and 141 | 19740 |
| 138 and 192 | 4416 |