Least Common Multiple (LCM) of 83 and 147
The least common multiple (LCM) of 83 and 147 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 83 and 147?
First, calculate the GCD of 83 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 147 = 0 remainder 83 |
| 2 | 147 ÷ 83 = 1 remainder 64 |
| 3 | 83 ÷ 64 = 1 remainder 19 |
| 4 | 64 ÷ 19 = 3 remainder 7 |
| 5 | 19 ÷ 7 = 2 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 103 | 7107 |
| 192 and 20 | 960 |
| 152 and 21 | 3192 |
| 109 and 195 | 21255 |
| 108 and 157 | 16956 |