Least Common Multiple (LCM) of 75 and 106
The least common multiple (LCM) of 75 and 106 is 7950.
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 106?
First, calculate the GCD of 75 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 106 = 0 remainder 75 |
| 2 | 106 ÷ 75 = 1 remainder 31 |
| 3 | 75 ÷ 31 = 2 remainder 13 |
| 4 | 31 ÷ 13 = 2 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 161 | 15456 |
| 120 and 61 | 7320 |
| 114 and 51 | 1938 |
| 90 and 74 | 3330 |
| 70 and 43 | 3010 |