Least Common Multiple (LCM) of 21 and 112
The least common multiple (LCM) of 21 and 112 is 336.
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 112?
First, calculate the GCD of 21 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 112 = 0 remainder 21 |
| 2 | 112 ÷ 21 = 5 remainder 7 |
| 3 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 76 | 10716 |
| 197 and 101 | 19897 |
| 102 and 49 | 4998 |
| 135 and 88 | 11880 |
| 157 and 49 | 7693 |