Least Common Multiple (LCM) of 147 and 83
The least common multiple (LCM) of 147 and 83 is 12201.
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 83?
First, calculate the GCD of 147 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 147 ÷ 83 = 1 remainder 64 |
| 2 | 83 ÷ 64 = 1 remainder 19 |
| 3 | 64 ÷ 19 = 3 remainder 7 |
| 4 | 19 ÷ 7 = 2 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 22 | 2310 |
| 68 and 102 | 204 |
| 35 and 27 | 945 |
| 65 and 90 | 1170 |
| 170 and 134 | 11390 |