Find the LCM of $6 m^{2} - 3 m - 45, 6 m^{2} + 11 m - 10$

Open in App

Solution

We know that $L C M$ is the least common multiple.

Factorise $6 m^{2} - 3 m - 45$ as follows:

$6 m^{2} - 3 m - 45 = 3 (2 m^{2} - m - 15) = 3 (2 m^{2} - 6 m + 5 m - 15) = 3 [2 m (m - 3) + 5 (m - 3)] = 3 (2 m + 5) (m - 3)$

Now, factorise $6 m^{2} + 11 m - 10$ as follows:

$6 m^{2} + 11 m - 10 = 6 m^{2} + 15 m - 4 m - 10 = 3 m (2 m + 5) - 2 (2 m + 5) = (3 m - 2) (2 m + 5)$

Therefore, the least common multiple between the polynomials $6 m^{2} - 3 m - 45$ and $6 m^{2} + 11 m - 10$ is:

$L C M = 3 (m - 3) (2 m + 5) (3 m - 2)$

Hence, the $L C M$ is $3 (m - 3) (2 m + 5) (3 m - 2)$ .

Suggest Corrections

Similar questions

6 m^{2} - 11 m + 6 = 0

(6 m^{3} - 17 m^{2} - 5 m + 6)

(6 m^{3} - 5 m^{2} - 3 m + 2)

5 m^{2} + 3 m + 8; m^{3} - 6 m^{2} + 4 m; m^{3} - m^{2} - m + 5

5 m, (3 m - 5)

{6 m}^{2} - 13 m

3 m

1.7 \times 10^{- 6} m^{2}

3 \times 10^{- 2} m^{2}

Join BYJU'S Learning Program