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If the HCF and the LCM of two numbers are 7 and 245, respectively, then their product is:
1517
1175
1751
1715
1715
Use the fundamental property that the product of any two positive integers always equals the product of their HCF and LCM.
HCF of two numbers = 7, LCM of two numbers = 245
Product┬аof┬аtwo┬аnumbers=HCF├ЧLCM
Use the fundamental property that the product of any two positive integers always equals the product of their HCF and LCM.
Confusing HCF and LCM or trying to find the numbers individually, which is unnecessary and time-consuming.
State the standard formula
For any two positive integers a and b, the product of the numbers is equal to the product of their Highest Common Factor (HCF) and Least Common Multiple (LCM).
Product=HCF├ЧLCM
Substitute the given values
Given that the HCF is 7 and the LCM is 245, substitute these values into the formula: Product=7├Ч245.
Product=7├Ч245
Calculate the final product
Multiply 7 by 245: 7├Ч200=1400, 7├Ч40=280, 7├Ч5=35, summing them up gives 1400+280+35=1715.
1715
D is correct because the product of two numbers is equal to the product of their HCF and LCM, which equals 7├Ч245=1715.
This fundamental relation HCF(a,b)├ЧLCM(a,b)=a├Чb is exclusively valid for two numbers and frequently tested in competitive exams.