Least Common Multiple (LCM) of 107 and 147
The least common multiple (LCM) of 107 and 147 is 15729.
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 107 and 147?
First, calculate the GCD of 107 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 147 = 0 remainder 107 |
| 2 | 147 ÷ 107 = 1 remainder 40 |
| 3 | 107 ÷ 40 = 2 remainder 27 |
| 4 | 40 ÷ 27 = 1 remainder 13 |
| 5 | 27 ÷ 13 = 2 remainder 1 |
| 6 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 73 | 3942 |
| 193 and 75 | 14475 |
| 69 and 26 | 1794 |
| 38 and 118 | 2242 |
| 44 and 127 | 5588 |