How do you use prime factorizations to find the LCM of 28 and 42?

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How do you use prime factorizations to find the LCM of 28 and 42?

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Answer 1 · 2016-08-01T04:00:22

$L C M = 84$ $LCM=84$

Explanation:

Prime factors of $28$ $28$ and $42$ $42$ are as follows

$28 = 2 \times 2 \times 7$ $28=2xx2xx7$ and

$42 = 2 \times 3 \times 7$ $42=2xx3xx7$

Now it is observed that

$2$ $2$ occurs maximum $2$ $2$ times
$3$ $3$ occurs maximum $1$ $1$ time
$7$ $7$ occurs maximum $1$ $1$ time

Hence $L C M = 2 \times 2 \times 3 \times 7 = 84$ $LCM=2xx2xx3xx7=84$

Answer 2 · 2016-08-01T15:53:00

LCM= $= 2 \times 2 \times 3 \times 7 = 84$ $" " = 2xx2xx3xx7 = 84$

Explanation:

The importance and use of prime factors are really under-estimated.

If you have a number written as the product of its prime factors, then you know EVERYTHING about that number.

As soon as the factors $2 \times 2 \times 7$ $2 xx 2xx 7$ appear anywhere it means that 28 is there.

Similarly, 42 is made up of $2 \times 3 \times 7$ $2 xx 3 xx 7$

Any number which is to be divisible by both of theses numbers has to have all of the factors for each number, but without the duplicates.
Writing them in the following format makes it easy to see what the factors of the LCM are. It is also an easy way of finding the highest common factor.

$28 = 2 \times 2 \times \times x 7$ $" "28 = 2xx2xxcolor(white)(xxx)7$
$42 = 2 \times 2 \times 3 \times 7$ $" "42 = 2xxcolor(white)(2xx)3 xx 7$

LCM= $= 2 \times 2 \times 3 \times 7 = 84$ $" " = 2xx2xx3xx7 = 84$

HCF= $= 2 \times \times \times \times 7 = 14$ $" "=2xxcolor(white)(xxxxxx)7 =14$

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How do you use prime factorizations to find the LCM of 28 and 42?

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