Least Common Multiple (LCM) of 109 and 147
The least common multiple (LCM) of 109 and 147 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 109 and 147?
First, calculate the GCD of 109 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 147 = 0 remainder 109 |
| 2 | 147 ÷ 109 = 1 remainder 38 |
| 3 | 109 ÷ 38 = 2 remainder 33 |
| 4 | 38 ÷ 33 = 1 remainder 5 |
| 5 | 33 ÷ 5 = 6 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 66 | 1254 |
| 169 and 14 | 2366 |
| 17 and 112 | 1904 |
| 18 and 162 | 162 |
| 173 and 89 | 15397 |