Least Common Multiple (LCM) of 150 and 21
The least common multiple (LCM) of 150 and 21 is 1050.
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 150 and 21?
First, calculate the GCD of 150 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 21 = 7 remainder 3 |
| 2 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 197 | 37824 |
| 125 and 99 | 12375 |
| 125 and 119 | 14875 |
| 36 and 19 | 684 |
| 13 and 28 | 364 |