Least Common Multiple (LCM) of 105 and 28
The least common multiple (LCM) of 105 and 28 is 420.
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 105 and 28?
First, calculate the GCD of 105 and 28 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 28 = 3 remainder 21 |
| 2 | 28 ÷ 21 = 1 remainder 7 |
| 3 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 39 | 2340 |
| 63 and 40 | 2520 |
| 129 and 62 | 7998 |
| 121 and 112 | 13552 |
| 180 and 115 | 4140 |