The least common multiple, or LCM, of 35 and 10 is 70. Use prime factorization of both numbers to find the least common multiple. Prime factorization involves finding the prime numbers that multiply together to yield a particular number.
Prime numbers are numbers greater than one that are evenly divisible by only themselves and one. The prime factorization of 10 is 2 x 5. The prime factorization of 35 is 5 x 7. Multiply the prime factors together using each one the greatest number of times it is used in either prime factorization. In this case, multiply 2 x 5 x 7. The product is 70. Use only one of the fives because it is common to both 10 and 35, and the greatest number of times it is used with either one is once.