If r , s , t are different prime numbers and a , b , c are the positive integers such that LCM of a , b, c is r2 s4 t2 and HCF of a, b, c is r s2 t, then the number of ordered triplets (a, b, c) is

Question

If r , s , t are different prime numbers and a , b , c are the positive integers such that LCM of a , b, c is r2 s4 t2 and HCF of a, b, c is r s2 t, then the number of ordered triplets (a, b, c) is (A) 248 (B) 432 (C) 648 (D) 931

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/89d90e7150d69d0da56ceb6e0553f2e4-.png" /> Total ways 6 × 6 × 12 = 432

Q. If $r, s, t$ are different prime numbers and $a, b, c$ are the positive integers such that $L CM$ of $a, b$ , c is $r^{2} s^{4} t^{2}$ and HCF of $a, b, c$ is $r s^{2} t$ , then the number of ordered triplets $(a, b, c)$ is

248

432

648

931

Total ways $6 \times 6 \times 12 = 432$

Q. If r,s,t are different prime numbers and a,b,c are the positive integers such that LCM of a,b, c is r2s4t2 and HCF of a,b,c is rs2t, then the number of ordered triplets (a,b,c) is

248

432

648

931

Total ways 6×6×12=432

Q. If $r, s, t$ are different prime numbers and $a, b, c$ are the positive integers such that $L CM$ of $a, b$ , c is $r^{2} s^{4} t^{2}$ and HCF of $a, b, c$ is $r s^{2} t$ , then the number of ordered triplets $(a, b, c)$ is

Total ways $6 \times 6 \times 12 = 432$