Least Common Multiple (LCM) of 85 and 147
The least common multiple (LCM) of 85 and 147 is 12495.
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 85 and 147?
First, calculate the GCD of 85 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 147 = 0 remainder 85 |
| 2 | 147 ÷ 85 = 1 remainder 62 |
| 3 | 85 ÷ 62 = 1 remainder 23 |
| 4 | 62 ÷ 23 = 2 remainder 16 |
| 5 | 23 ÷ 16 = 1 remainder 7 |
| 6 | 16 ÷ 7 = 2 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 53 | 5353 |
| 113 and 10 | 1130 |
| 144 and 43 | 6192 |
| 127 and 10 | 1270 |
| 45 and 153 | 765 |