Least Common Multiple (LCM) of 67 and 147
The least common multiple (LCM) of 67 and 147 is 9849.
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 147?
First, calculate the GCD of 67 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 147 = 0 remainder 67 |
| 2 | 147 ÷ 67 = 2 remainder 13 |
| 3 | 67 ÷ 13 = 5 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 64 | 1728 |
| 98 and 120 | 5880 |
| 120 and 112 | 1680 |
| 38 and 197 | 7486 |
| 83 and 103 | 8549 |