Least Common Multiple (LCM) of 74 and 103
The least common multiple (LCM) of 74 and 103 is 7622.
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 74 and 103?
First, calculate the GCD of 74 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 103 = 0 remainder 74 |
| 2 | 103 ÷ 74 = 1 remainder 29 |
| 3 | 74 ÷ 29 = 2 remainder 16 |
| 4 | 29 ÷ 16 = 1 remainder 13 |
| 5 | 16 ÷ 13 = 1 remainder 3 |
| 6 | 13 ÷ 3 = 4 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 39 | 195 |
| 191 and 178 | 33998 |
| 67 and 122 | 8174 |
| 70 and 121 | 8470 |
| 174 and 147 | 8526 |