Least Common Multiple (LCM) of 156 and 175
The least common multiple (LCM) of 156 and 175 is 27300.
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 156 and 175?
First, calculate the GCD of 156 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 175 = 0 remainder 156 |
| 2 | 175 ÷ 156 = 1 remainder 19 |
| 3 | 156 ÷ 19 = 8 remainder 4 |
| 4 | 19 ÷ 4 = 4 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 140 | 9660 |
| 108 and 180 | 540 |
| 52 and 115 | 5980 |
| 19 and 160 | 3040 |
| 200 and 128 | 3200 |