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

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

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