Least Common Multiple (LCM) of 21 and 175
The least common multiple (LCM) of 21 and 175 is 525.
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 21 and 175?
First, calculate the GCD of 21 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 175 = 0 remainder 21 |
| 2 | 175 ÷ 21 = 8 remainder 7 |
| 3 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 22 | 1408 |
| 100 and 141 | 14100 |
| 54 and 60 | 540 |
| 132 and 180 | 1980 |
| 102 and 77 | 7854 |