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 |
|---|---|
| 126 and 100 | 6300 |
| 111 and 154 | 17094 |
| 174 and 35 | 6090 |
| 160 and 117 | 18720 |
| 157 and 65 | 10205 |