Least Common Multiple (LCM) of 75 and 119
The least common multiple (LCM) of 75 and 119 is 8925.
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 119?
First, calculate the GCD of 75 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 119 = 0 remainder 75 |
| 2 | 119 ÷ 75 = 1 remainder 44 |
| 3 | 75 ÷ 44 = 1 remainder 31 |
| 4 | 44 ÷ 31 = 1 remainder 13 |
| 5 | 31 ÷ 13 = 2 remainder 5 |
| 6 | 13 ÷ 5 = 2 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 126 | 12726 |
| 99 and 156 | 5148 |
| 108 and 169 | 18252 |
| 55 and 105 | 1155 |
| 167 and 184 | 30728 |