I saw some formulas regarding HCF and LCM and I am unable to prove them still.
Try if you can, if yes then please write it in the comments
\(LCM(a,b,c)=\frac{a×b×c×HCF(a,b,c)}{HCF(a,b)×HCF(b,c)×HCF(c,a)}\)
HCF(a,b,c)=LCM(a,b)×LCM(b,c)×LCM(c,a)a×b×c×LCM(a,b,c)
LCMoffractions=HCFofdenominatorsLCMofnumerators
HCFoffractions=LCMofdenominatorsHCFofnumerators
Try to prove them
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I can prove the first two formulas. Consider the primes that divide a, b , and c. If we show that the powers of each prime on both sides of the equation are the same, then both sides of the equation are equal. Take some prime p. Say that pk1∣a, pk2∣b, and pk3∣c, with k1≤k2≤k3. Then, the exponent of p on the left hand side is k3. The exponent on the right hand side is k1+k2+k3+k1−k1−k2−k1=k3, so both sides are equal. The proof of the second formula is similar.
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Thanks for the proof