Least Common Multiple (LCM) of 21 and 153
The least common multiple (LCM) of 21 and 153 is 1071.
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 153?
First, calculate the GCD of 21 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 153 = 0 remainder 21 |
| 2 | 153 ÷ 21 = 7 remainder 6 |
| 3 | 21 ÷ 6 = 3 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 102 | 3162 |
| 113 and 135 | 15255 |
| 93 and 98 | 9114 |
| 162 and 89 | 14418 |
| 40 and 103 | 4120 |