НОК(42,49)

To find the least common multiple (LCM) of two numbers, such as 42 and 49, you can use the prime factorization method or the division method.

Prime factorization method:

1. Prime factorize both numbers:
   • For 42: 2 × 3 × 7
   • For 49: 7 × 7
2. Take the highest power of each prime factor:
   • 2 × 3 × 7 × 7 = 294
3. So, the LCM of 42 and 49 is 294.

Division method:

1. Start by dividing one number (42) by the other number (49).
   • 49 divides 42 zero times with a remainder of 42.
2. Then, divide the divisor (49) by the remainder (42).
   • 42 divides 49 once with a remainder of 7.
3. Divide the new remainder (7) by the previous remainder (42).
   • 7 divides 42 six times with a remainder of 0.
4. The quotient from Step 3 is the LCM of 42 and 49.
   • The quotient is 6.
5. Multiply the quotient by the divisor (49) to get the LCM.
   • 6 × 49 = 294.
6. So, the LCM of 42 and 49 is 294.

Therefore, the LCM of 42 and 49 is 294.