Tag: lcm

Taking out the factors of the given numbers,

$36 = 2 \times 2 \times 3 \times 3$
$72 = 2 \times 2 \times 2 \times 3 \times 3$
$\therefore $ L.C.M of $36$  and $72$  $= 2 \times 2 \times 2 \times 3 \times 3 = 72$

Multiples of $ 18 = 18, 36, 54...$
Multiples of $ 6 = 6, 12, 18, ... $
The first common multiple will be $ 18 $
And the next common multiples will be multiples of $ 18 $
Hence, first three common multiples of $ 18, 6 $ are $ 18, 36, 54 $

Factors of the given numbers are,

Factors are $ 17 = 1 \times 17$
$5 = 1 \times 5 $
$\therefore $ LCM of $17$ and $5$  $= 1 \times 17 \times 5 = 85$

LCM of two co -prime numbers is their product.
Example: Consider $6$ and $7,$
Multiple of $6$ $ = 6,12,18,24,30,36,42, 48$
Multiple of $7$ $= 7,14,21,28,35,42$
L.C.M of $6$ and $7$ $= 42$
The product of $6$ and $7$ $= 6 \times 7 = 42$

$12\times 1=12$
$12\times 3=36$
$\therefore 12$ and $36$ are multiples,

Multiples of $14$ are $14\times 1, 14\times 2$ ....
And $7$ and $1$ are the factors of $14$.

$LCM \times HCF =$ product of numbers

$p = 4, 4\div 2 = 2$
$p + 2 = 4 +2, 6\div 2 = 3$
$p + 4 = 4 + 4, 8\div 2 = 4$
Product is divisible by $2.$
Therefore, $C$ is the correct answer.