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 |
|---|---|
| 155 and 64 | 9920 |
| 148 and 136 | 5032 |
| 33 and 137 | 4521 |
| 169 and 196 | 33124 |
| 189 and 12 | 756 |