Least Common Multiple (LCM) of 71 and 104
The least common multiple (LCM) of 71 and 104 is 7384.
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 71 and 104?
First, calculate the GCD of 71 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 104 = 0 remainder 71 |
| 2 | 104 ÷ 71 = 1 remainder 33 |
| 3 | 71 ÷ 33 = 2 remainder 5 |
| 4 | 33 ÷ 5 = 6 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 45 | 5310 |
| 167 and 30 | 5010 |
| 120 and 121 | 14520 |
| 144 and 193 | 27792 |
| 141 and 24 | 1128 |