Least Common Multiple (LCM) of 152 and 175
The least common multiple (LCM) of 152 and 175 is 26600.
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 152 and 175?
First, calculate the GCD of 152 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 175 = 0 remainder 152 |
| 2 | 175 ÷ 152 = 1 remainder 23 |
| 3 | 152 ÷ 23 = 6 remainder 14 |
| 4 | 23 ÷ 14 = 1 remainder 9 |
| 5 | 14 ÷ 9 = 1 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 60 | 6180 |
| 17 and 72 | 1224 |
| 142 and 170 | 12070 |
| 69 and 12 | 276 |
| 169 and 146 | 24674 |