find the LCM and HCF of 243 and 729 and verify that lCM×HCF=product of the two numbers
Answers
Answer:
To Verify:
- LCM × HCF = a × b
where, 'a' and 'b' are the given two numbers ( 243 & 729 )
Applying Prime factorisation for 243 and 729 we get:
→ 243 = 3 × 3 × 3 × 3 × 3 = 3⁵
→ 729 = 3 × 3 × 3 × 3 × 3 × 3 = 3⁶
Now HCF refers to the common factors between two numbers. In terms of Power, the least power of both is taken as HCF.
In the above question, the least power among both is 3⁵. Hence the HCF of the number is 3⁵ which is 243.
Coming to LCM, it refers to highest power of common terms between two numbers. In the above case, the highest power of the common term 3 is 3⁶. Hence the LCM of both the numbers is 3⁶ which is 729.
Hence multiplying HCF and LCM we get:
⇒ HCF × LCM = 3⁵ × 3⁶ = 243 × 729 = a × b
Hence LHS = RHS
Hence verified !!
Answer:
243 × 729= LCM of numbers ×HCF of numbers
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