19. 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 20. The least common multiple of two numbers is 168 and their highest common factor is 12. If the difference between the numbers is 60, what is the sum of the numbers? (a) 108 (b) 96 (c) 122 (d) 144
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If the HCF of the two numbers is 23, then let the two numbers be 23x and 23y.
The LCM of these two numbers can be written as 23xy.
Since the other two factors of LCM are 13 and 14,
therefore the values of x and y are 13 and 14 respectively.
So, the largest number is 23y,
23y = 23 × 14 = 322
Step-by-step explanation:
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