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Prove that √2 is an irrational number.
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.
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 ?
Find the smallest number which is divisible by both 644 and 462.
Two numbers are in the ratio 4 : 5 and their HCF is 11. Find the LCM of these numbers.
State the "Fundamental Theorem of Arithmetic" and use it to find LCM of 36 and 54.
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