Least Common Multiple (LCM) of 21 and 142
The least common multiple (LCM) of 21 and 142 is 2982.
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 142?
First, calculate the GCD of 21 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 142 = 0 remainder 21 |
| 2 | 142 ÷ 21 = 6 remainder 16 |
| 3 | 21 ÷ 16 = 1 remainder 5 |
| 4 | 16 ÷ 5 = 3 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 42 | 336 |
| 118 and 104 | 6136 |
| 196 and 152 | 7448 |
| 49 and 95 | 4655 |
| 145 and 164 | 23780 |