The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14. The larger of the two numbers is :
The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14. The larger of the two numbers is :
[A]276
[B]299
[C]322
[D]345
322
Let the numbers be 23x and 23y where x and y are co-prime to each other.
∴ LCM = 23xy
As given,
23xy = 23 $latex \times$ 13 $latex \times$ 14
∴ x = 13, y = 14
∴ The larger number = 23y = 23 $latex \times$ 14 = 322
Hence option [C] is correct answer.