Least Common Multiple (LCM) of 75 and 49
The least common multiple (LCM) of 75 and 49 is 3675.
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 75 and 49?
First, calculate the GCD of 75 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 49 = 1 remainder 26 |
| 2 | 49 ÷ 26 = 1 remainder 23 |
| 3 | 26 ÷ 23 = 1 remainder 3 |
| 4 | 23 ÷ 3 = 7 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 57 | 1995 |
| 149 and 84 | 12516 |
| 120 and 106 | 6360 |
| 161 and 190 | 30590 |
| 176 and 72 | 1584 |