Least Common Multiple (LCM) of 175 and 149
The least common multiple (LCM) of 175 and 149 is 26075.
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 175 and 149?
First, calculate the GCD of 175 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 149 = 1 remainder 26 |
| 2 | 149 ÷ 26 = 5 remainder 19 |
| 3 | 26 ÷ 19 = 1 remainder 7 |
| 4 | 19 ÷ 7 = 2 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 160 | 7840 |
| 160 and 82 | 6560 |
| 106 and 153 | 16218 |
| 191 and 99 | 18909 |
| 28 and 116 | 812 |