using lambda instead of let in scheme

In SICP 1.2.1 there is a function that makes a rational number, as follow:

(define (make-rat n d)
  (let ((g (gcd n d)))
    (cons (/ n g) (/ d g))))

I'm just curious how you can implement the same thing using lambda instead of let, without calling GCD twice. I couldn't figure it out myself.

Solution

(let ((<var1> <exp1>)
      (<var2> <exp2>)
      ...
      (<varn> <expn>))
   <body>)

is equivalent to

((lambda (<var1> ...<varn>)
    <body>)
 <exp1>
 ...
 <expn>)

So your procedure,

(define (make-rat n d)
  (let ((g (gcd n d)))
    (cons (/ n g) (/ d g))))

should be equivalent to

(define (make-rat n d)
  ((lambda (g)
    (cons (/ n g) (/ d g)))
  (gcd n d)))