l.c.m of two numbers is p^2 q^4 r^4 p q r are primes.find the possible no. of pairs


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Question Number 87586 by manr last updated on 05/Apr/20

$l . c . m o f t w o n u m b e r s i s p^{2} q^{4} r^{4} p q r a r e$ $p r i m e s . f i n d t h e p o s s i b l e n o . o f p a i r s$
	Answered by mr W last updated on 05/Apr/20

	$l c m (x, y) = p^{2} q^{4} r^{4}$ $s a y x = p^{i} q^{j} r^{k} w i t h i, j, k ⩾ 0$ $s a y y = p^{a} q^{b} r^{c} w i t h a, b, c ⩾ 0$ $m a x (i, a) = 2 \Rightarrow 2 \times 3 = 6 p o s s i b l i t i e s$ $m a x (j, b) = 4 \Rightarrow 2 \times 5 = 10 p o s s i b l i t i e s$ $m a x (k, c) = 4 \Rightarrow 2 \times 5 = 10 p o s s i b l i t i e s$ $\Rightarrow 6 \times 10 \times 10 = 600 p o s s i b l e p a i r s f o r x, y .$
	Commented by mr W last updated on 05/Apr/20

	$M J S s i r : i s t h i s c o r r e c t ?$
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