Least Common Multiple (LCM) of 85 and 148
The least common multiple (LCM) of 85 and 148 is 12580.
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 148?
First, calculate the GCD of 85 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 148 = 0 remainder 85 |
| 2 | 148 ÷ 85 = 1 remainder 63 |
| 3 | 85 ÷ 63 = 1 remainder 22 |
| 4 | 63 ÷ 22 = 2 remainder 19 |
| 5 | 22 ÷ 19 = 1 remainder 3 |
| 6 | 19 ÷ 3 = 6 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 169 | 18421 |
| 68 and 62 | 2108 |
| 118 and 91 | 10738 |
| 21 and 120 | 840 |
| 31 and 54 | 1674 |