Question

the lcm of two numbers is 1600. which of the following cannot be their HCF? 400,100,500,200​

Answer 1

➢ Answer :

500 cannot be the HCF of the two numbers.

➢ Given :

LCM of the two numbers = 1600

➢ To Find :

The number which cannot exist as the HCF of the two numbers.

➢ How To Find :

We know HCF of n numbers divides its LCM exactly.

Now,

▶ Case I :

⇝ HCF = 400

⇝ LCM = 1600

⇝ LCM/HCF = 1600/400 = 4.

Hence, 400 can be the HCF of the two numbers.

▶ Case II :

⇝ HCF = 100

⇝ LCM = 1600

⇝ LCM/HCF = 1600/100 = 16.

Hence, 100 can be the HCF of the two numbers.

▶ Case III :

⇝ HCF = 500

⇝ LCM = 1600

⇝ LCM/HCF = 1600/500 = 3.2

Hence, 500 cannot be the HCF of the two numbers.

▶ Case IV :

⇝ HCF = 200

⇝ LCM = 1600

⇝ LCM/HCF = 1600/200 = 8.

Hence, 200 can also be the HCF of the two numbers.

∴ The only number which cannot be the HCF of the two numbers is 500.

Answer 2

Answer:

500 is the answer

MARKE AS BRAINILIEST