Least Common Multiple (LCM) of 162 and 21
The least common multiple (LCM) of 162 and 21 is 1134.
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 162 and 21?
First, calculate the GCD of 162 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 21 = 7 remainder 15 |
| 2 | 21 ÷ 15 = 1 remainder 6 |
| 3 | 15 ÷ 6 = 2 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 53 | 1908 |
| 133 and 174 | 23142 |
| 116 and 160 | 4640 |
| 63 and 61 | 3843 |
| 178 and 60 | 5340 |