Least Common Multiple (LCM) of 105 and 147
The least common multiple (LCM) of 105 and 147 is 735.
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 105 and 147?
First, calculate the GCD of 105 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 147 = 0 remainder 105 |
| 2 | 147 ÷ 105 = 1 remainder 42 |
| 3 | 105 ÷ 42 = 2 remainder 21 |
| 4 | 42 ÷ 21 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 129 | 11739 |
| 77 and 72 | 5544 |
| 164 and 195 | 31980 |
| 15 and 96 | 480 |
| 118 and 81 | 9558 |