Question

The LCM of 2³×3² and 2²×3³ is
(with steps)​

Answer 1

•Step-by-step explanation!!

2³x3² and 2²x3³ LCM is

2×2×2×3×3 (1).

2×2×3×3×3 (2).

So, in LCM we take the maximum power

2x2x2x3x3x3 then answer will be 2³×3³.

Answer 2

Answer:

LCM of 2³ × 3² and 2² × 3³ is 2³ × 3³

Step-by-step explanation:

Step:1The LCM is $2^3 \times 3^3$

Given two numbers

$2^3 \times 3^2$ and$2^2 \times 3^3$

We must calculate the LCM of the previous two values.

The lowest number into which two numbers may be divided equally is called the least common multiple, or LCM.

The highest exponent number from both numbers must be multiplied in order to determine the LCM.

$\begin{aligned}& 2^3 \times 3^2=2 \times 2 \times 2 \times 3 \times 3 \\& 2^2 \times 3^3=2 \times 2 \times 3 \times 3 \times 3 \\& L C M\left(2^3 \times 3^2, 2^2 \times 3^3\right)=2^3 \times 3^3\end{aligned}$

which is required LCM.

Step:2 Write down the given numbers

First number = 2³ × 3²

Second number = 2² × 3³

2 , 3 are the prime numbers present in the prime factorisation of the given numbers

From the given two numbers

Highest power of 2 = 3

Highest power of 3 = 3

The required LCM

= The product of highest powers of all prime factors

= 2³ × 3³

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