LCM of (5⁴ × 7 × 11) and (5² × 7² × 11²) is :

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MCQ (Single)Fundamental Theorem of ArithmeticLCM Using Prime Factorisation Method

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Prove that √3 is an irrational number.

TextFundamental Theorem of ArithmeticPrime Factorisation of Natural NumbersIrrationality of Square Root of Prime NumbersProof by Contradiction Method

Fundamental Theorem of Arithmetic

Prime Factorisation of Natural Numbers

Irrationality of Square Root of Prime Numbers

Proof by Contradiction Method

State true or false for each of the following statements and justify in each case :

CASE_STUDIESFundamental Theorem of ArithmeticPrime Factorisation of Natural NumbersIrrationality of Square Root of Prime NumbersProof by Contradiction Method

If x = ab³ and y = a³b, where a and b are prime numbers, then [HCF (x, y) – LCM (x, y)] is equal to :

MCQ (Single)HCF Using Prime Factorisation MethodLCM Using Prime Factorisation Method

Prove that √2 is an irrational number.

TextHCF Using Prime Factorisation MethodLCM Using Prime Factorisation MethodRelationship Between HCF and LCM of Two NumbersIrrationality of Square Root of Prime NumbersProof by Contradiction MethodHCF Using Prime Factorisation MethodLCM Using Prime Factorisation MethodRelationship Between HCF and LCM of Two NumbersIrrationality of Square Root of Prime NumbersProof by Contradiction Method

Let x and y be two distinct prime numbers and p = x²y³, q = xy⁴, r = x⁵y². Find the HCF and LCM of p, q and r. Further check if HCF (p, q, r) × LCM (p, q, r) = p × q × r or not.

TextHCF Using Prime Factorisation MethodLCM Using Prime Factorisation MethodRelationship Between HCF and LCM of Two NumbersIrrationality of Square Root of Prime NumbersProof by Contradiction Method

If x is the LCM of 4, 6, 8 and y is the LCM of 3, 5, 7 and p is the LCM of x and y, then which of the following is true ?

MCQ (Single)LCM Using Prime Factorisation MethodRelationship Between HCF and LCM of Two Numbers