Must 1031 Like Kind Exchange = Sale Price or Greater to Qualify?

[Peter K.]

Using basic numbers, assuming I sell a property for $10M and after cost basis is accounted for and mortgage is paid off, I have a net taxable gain to me of $3M.

I'd like to purchase a rental lake house property for $1M (funds coming from that $3M taxable gain).  Is this possible to 1031 into?  I read a post on here that stated in order for it to qualify, the new purchase of the 1031 had to be of the total sale amount ($10M or greater).  I couldn't just use a portion of the taxable gain to purchase a less expensive property?

(The properties do qualify for like kind exchange.)

Thanks for any help/input!