Least Common Multiple (LCM) of 21 and 156
The least common multiple (LCM) of 21 and 156 is 1092.
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 156?
First, calculate the GCD of 21 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 156 = 0 remainder 21 |
| 2 | 156 ÷ 21 = 7 remainder 9 |
| 3 | 21 ÷ 9 = 2 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 102 | 1122 |
| 123 and 195 | 7995 |
| 107 and 74 | 7918 |
| 84 and 49 | 588 |
| 171 and 173 | 29583 |