Question

Find the least common multiple of 8x³y6z, 6x5z², and 10yzº.

Answer 1

Answer:

The Least Common Multiple (LCM) of $8x^3y6z,6x5z^2, \text{ and } 10yz^0 \text{ is } 240 x^3yz^2$

Step-by-step explanation:

Definition of LCM

The LCM of a, b , c is the smallest multiplier that is divisible by a, b and c

Here the three terms are :

$8x^3y6z$

$6x5z^2$

$10yz^0=10y$        since $z^0 = 1$

Factoring using prime factorization we get  $8x^3y6z = 2.2.2.x^3.y.2.3.z$³

= $2^4\cdot \:3\cdot \:x^3\cdot \:y\cdot \:z$   (1)

Factoring $6x5z^2$  we get

$2\cdot \:3\cdot \:5\cdot \:x\cdot \:z^2$  (2)

Factoring $10yz^0$ we get

$2 \;\cdot\; 5y$                 ($z^0 = 1)$   (3)

The LCM is the multiple of each of the highest power in each factor

$2^4\;.\;3\;.\;5\;.x^2\;.\;y\;.z^2 = 240 x^3yz^2$