If a, b, c, d are distinct prime numbers with a as smallest prime then a × b ×…

The smallest prime number is 2 — it is the only even prime number; every other prime number is odd. Whenever 2 appears as one of the factors in a product, that product is always even, because the factor of 2 is retained in the result regardless of the other factors.

Here, a, b, c, d are four distinct prime numbers, and a is given as the smallest among them.

1. Among all prime numbers, the smallest one is 2, so a = 2.

2. The product becomes a × b × c × d = 2 × b × c × d.

3. Since 2 is one of the factors, the product 2 × b × c × d is a multiple of 2 — an even number — no matter which distinct primes b, c, and d are.

Cross-check with actual numbers: take b, c, d as 3, 5, and 7 (three distinct primes different from a). Then a × b × c × d = 2 × 3 × 5 × 7 = 210, which is indeed even, confirming the reasoning.

Therefore, a × b × c × d is always an Even number.