Least Common Multiple (LCM) of 105 and 21
The least common multiple (LCM) of 105 and 21 is 105.
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 21?
First, calculate the GCD of 105 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 21 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 107 | 12840 |
| 186 and 113 | 21018 |
| 35 and 105 | 105 |
| 155 and 185 | 5735 |
| 96 and 127 | 12192 |