Least Common Multiple (LCM) of 147 and 109
The least common multiple (LCM) of 147 and 109 is 16023.
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 147 and 109?
First, calculate the GCD of 147 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 147 ÷ 109 = 1 remainder 38 |
| 2 | 109 ÷ 38 = 2 remainder 33 |
| 3 | 38 ÷ 33 = 1 remainder 5 |
| 4 | 33 ÷ 5 = 6 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 153 | 6579 |
| 51 and 102 | 102 |
| 13 and 19 | 247 |
| 67 and 100 | 6700 |
| 60 and 52 | 780 |