Least Common Multiple (LCM) of 75 and 169
The least common multiple (LCM) of 75 and 169 is 12675.
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 169?
First, calculate the GCD of 75 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 169 = 0 remainder 75 |
| 2 | 169 ÷ 75 = 2 remainder 19 |
| 3 | 75 ÷ 19 = 3 remainder 18 |
| 4 | 19 ÷ 18 = 1 remainder 1 |
| 5 | 18 ÷ 1 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 95 and 18 | 1710 |
| 135 and 188 | 25380 |
| 161 and 73 | 11753 |
| 95 and 193 | 18335 |
| 166 and 11 | 1826 |